sqrt B (should all be same)

Percentage Accurate: 54.2% → 100.0%

Time: 26.6s

Alternatives: 5

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: 54.2% 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 57.6%

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

   1. sqrt-prod 46.2%

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

4. Applied egg-rr 46.2%

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

   1. *-commutative 46.2%

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

6. Simplified 46.2%

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

   1. *-commutative 46.2%

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

   2. sqrt-prod 46.0%

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

   3. associate-*r* 46.0%

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

   4. sqrt-prod 57.4%

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

   5. unpow2 57.4%

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

   6. sqrt-prod 57.6%

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

   7. *-commutative 57.6%

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

   8. pow1/2 57.6%

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

8. Applied egg-rr 57.6%

   \[\leadsto \color{blue}{{\left(2 \cdot {x}^{2}\right)}^{0.5}} \]
9. Step-by-step derivation

   1. unpow1/2 57.6%

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

   2. count-2 57.6%

      \[\leadsto \sqrt{\color{blue}{{x}^{2} + {x}^{2}}} \]

   3. unpow2 57.6%

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

   4. unpow2 57.6%

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

   5. hypot-define 100.0%

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

10. Simplified 100.0%

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

Alternative 2: 7.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

double code(double x) {
	return x * (x * 2.0);
}

Fortran

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

Java

public static double code(double x) {
	return x * (x * 2.0);
}

Python

def code(x):
	return x * (x * 2.0)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.6%

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

   1. sqrt-prod 46.2%

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

4. Applied egg-rr 46.2%

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

   1. *-commutative 46.2%

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

6. Simplified 46.2%

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

   1. *-commutative 46.2%

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

   2. sqrt-prod 46.0%

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

   3. associate-*r* 46.0%

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

   4. sqrt-prod 57.4%

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

   5. unpow2 57.4%

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

   6. sqrt-prod 57.6%

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

   7. *-commutative 57.6%

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

   8. pow1/2 57.6%

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

8. Applied egg-rr 57.6%

   \[\leadsto \color{blue}{{\left(2 \cdot {x}^{2}\right)}^{0.5}} \]
9. Step-by-step derivation

   1. unpow1/2 57.6%

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

   2. count-2 57.6%

      \[\leadsto \sqrt{\color{blue}{{x}^{2} + {x}^{2}}} \]

   3. unpow2 57.6%

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

   4. unpow2 57.6%

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

   5. hypot-define 100.0%

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

10. Simplified 100.0%

    \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]
11. Step-by-step derivation

    1. hypot-undefine 57.6%

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

    2. flip-+ 0.0%

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

    3. difference-of-squares 0.0%

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

    4. +-inverses 0.0%

       \[\leadsto \sqrt{\frac{\left(x \cdot x + x \cdot x\right) \cdot \color{blue}{0}}{x \cdot x - x \cdot x}} \]

    5. metadata-eval 0.0%

       \[\leadsto \sqrt{\frac{\left(x \cdot x + x \cdot x\right) \cdot \color{blue}{\log 1}}{x \cdot x - x \cdot x}} \]

    6. +-inverses 0.0%

       \[\leadsto \sqrt{\frac{\left(x \cdot x + x \cdot x\right) \cdot \log 1}{\color{blue}{0}}} \]

    7. metadata-eval 0.0%

       \[\leadsto \sqrt{\frac{\left(x \cdot x + x \cdot x\right) \cdot \log 1}{\color{blue}{\log 1}}} \]

    8. associate-*r/ 0.0%

       \[\leadsto \sqrt{\color{blue}{\left(x \cdot x + x \cdot x\right) \cdot \frac{\log 1}{\log 1}}} \]

    9. metadata-eval 0.0%

       \[\leadsto \sqrt{\left(x \cdot x + x \cdot x\right) \cdot \frac{\color{blue}{0}}{\log 1}} \]

    10. +-inverses 0.0%

        \[\leadsto \sqrt{\left(x \cdot x + x \cdot x\right) \cdot \frac{\color{blue}{\left(x \cdot x\right) \cdot \left(x \cdot x\right) - \left(x \cdot x\right) \cdot \left(x \cdot x\right)}}{\log 1}} \]

    11. metadata-eval 0.0%

        \[\leadsto \sqrt{\left(x \cdot x + x \cdot x\right) \cdot \frac{\left(x \cdot x\right) \cdot \left(x \cdot x\right) - \left(x \cdot x\right) \cdot \left(x \cdot x\right)}{\color{blue}{0}}} \]

    12. +-inverses 0.0%

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

    13. flip-+ 6.9%

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

    14. sqrt-unprod 7.2%

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

    15. add-sqr-sqrt 7.2%

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

    16. distribute-lft-out 7.2%

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

    17. *-commutative 7.2%

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

    18. *-un-lft-identity 7.2%

        \[\leadsto \color{blue}{\left(1 \cdot \left(x + x\right)\right)} \cdot x \]

    19. distribute-rgt-out 7.2%

        \[\leadsto \color{blue}{\left(x \cdot 1 + x \cdot 1\right)} \cdot x \]

    20. distribute-lft-out 7.2%

        \[\leadsto \color{blue}{\left(x \cdot \left(1 + 1\right)\right)} \cdot x \]

    21. metadata-eval 7.2%

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

12. Applied egg-rr 7.2%

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

13. Final simplification 7.2%

    \[\leadsto x \cdot \left(x \cdot 2\right) \]
14. Add Preprocessing

Alternative 3: 5.4% accurate, 105.0× 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 57.6%

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

   1. sqrt-prod 46.2%

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

4. Applied egg-rr 46.2%

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

   1. *-commutative 46.2%

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

6. Simplified 46.2%

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

   1. *-commutative 46.2%

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

   2. sqrt-prod 46.0%

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

   3. associate-*r* 46.0%

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

   4. sqrt-prod 57.4%

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

   5. unpow2 57.4%

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

   6. sqrt-prod 57.6%

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

   7. *-commutative 57.6%

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

   8. pow1/2 57.6%

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

8. Applied egg-rr 57.6%

   \[\leadsto \color{blue}{{\left(2 \cdot {x}^{2}\right)}^{0.5}} \]
9. Step-by-step derivation

   1. unpow1/2 57.6%

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

   2. count-2 57.6%

      \[\leadsto \sqrt{\color{blue}{{x}^{2} + {x}^{2}}} \]

   3. unpow2 57.6%

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

   4. unpow2 57.6%

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

   5. hypot-define 100.0%

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

10. Simplified 100.0%

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

12. Applied egg-rr 0.0%

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

14. Simplified 5.6%

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

Alternative 4: 5.4% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ 64 \end{array} \]

FPCore

(FPCore (x) :precision binary64 64.0)

C

double code(double x) {
	return 64.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 64.0d0
end function

Java

public static double code(double x) {
	return 64.0;
}

Python

def code(x):
	return 64.0

Julia

function code(x)
	return 64.0
end

MATLAB

function tmp = code(x)
	tmp = 64.0;
end

Wolfram

code[x_] := 64.0

Derivation

1. Initial program 57.6%

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

   1. sqrt-prod 46.2%

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

4. Applied egg-rr 46.2%

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

   1. *-commutative 46.2%

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

6. Simplified 46.2%

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

   1. *-commutative 46.2%

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

   2. sqrt-prod 46.0%

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

   3. associate-*r* 46.0%

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

   4. sqrt-prod 57.4%

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

   5. unpow2 57.4%

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

   6. sqrt-prod 57.6%

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

   7. *-commutative 57.6%

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

   8. pow1/2 57.6%

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

8. Applied egg-rr 57.6%

   \[\leadsto \color{blue}{{\left(2 \cdot {x}^{2}\right)}^{0.5}} \]
9. Step-by-step derivation

   1. unpow1/2 57.6%

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

   2. count-2 57.6%

      \[\leadsto \sqrt{\color{blue}{{x}^{2} + {x}^{2}}} \]

   3. unpow2 57.6%

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

   4. unpow2 57.6%

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

   5. hypot-define 100.0%

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

10. Simplified 100.0%

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

12. Applied egg-rr 0.0%

    \[\leadsto \color{blue}{{\left(\frac{0}{0}\right)}^{6}} \]

14. Simplified 5.6%

    \[\leadsto \color{blue}{64} \]
15. Add Preprocessing

Alternative 5: 5.4% accurate, 105.0× 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 57.6%

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

   1. sqrt-prod 46.2%

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

4. Applied egg-rr 46.2%

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

   1. *-commutative 46.2%

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

6. Simplified 46.2%

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

   1. *-commutative 46.2%

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

   2. sqrt-prod 46.0%

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

   3. associate-*r* 46.0%

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

   4. sqrt-prod 57.4%

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

   5. unpow2 57.4%

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

   6. sqrt-prod 57.6%

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

   7. *-commutative 57.6%

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

   8. pow1/2 57.6%

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

8. Applied egg-rr 57.6%

   \[\leadsto \color{blue}{{\left(2 \cdot {x}^{2}\right)}^{0.5}} \]
9. Step-by-step derivation

   1. unpow1/2 57.6%

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

   2. count-2 57.6%

      \[\leadsto \sqrt{\color{blue}{{x}^{2} + {x}^{2}}} \]

   3. unpow2 57.6%

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

   4. unpow2 57.6%

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

   5. hypot-define 100.0%

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

10. Simplified 100.0%

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

12. Applied egg-rr 0.0%

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

14. Simplified 5.6%

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

Reproduce

herbie shell --seed 2024099 
(FPCore (x)
  :name "sqrt B (should all be same)"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))