sqrt A (should all be same)

Percentage Accurate: 54.0% → 100.0%

Time: 1.5s

Alternatives: 3

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: 54.0% 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 54.4%

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

   1. hypot-def 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. Final simplification 100.0%

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

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 54.4%

   \[\sqrt{x \cdot x + x \cdot x} \]

2. Taylor expanded in x around 0 50.9%

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

4. Simplified 11.1%

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

5. Final simplification 11.1%

   \[\leadsto x + x \]

Alternative 3: 1.7% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -2.0)

C

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

Fortran

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

Java

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

Python

def code(x):
	return -2.0

Julia

function code(x)
	return -2.0
end

MATLAB

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

Wolfram

code[x_] := -2.0

Derivation

1. Initial program 54.4%

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

   1. flip-+ 0.0%

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

   2. difference-of-squares 0.0%

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

   3. associate-*r/ 0.0%

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

   4. +-inverses 0.0%

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

   5. +-inverses 0.0%

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

   6. flip-+ 6.8%

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

   7. sqrt-unprod 7.0%

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

   8. add-sqr-sqrt 7.0%

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

   9. expm1-log1p-u 7.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot x + x \cdot x\right)\right)} \]

   10. expm1-udef 6.3%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x \cdot x + x \cdot x\right)} - 1} \]

3. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\left(1 + \frac{0}{0}\right) - 1} \]

5. Simplified 1.7%

   \[\leadsto \color{blue}{-2} \]

6. Final simplification 1.7%

   \[\leadsto -2 \]

Reproduce

herbie shell --seed 2023203 
(FPCore (x)
  :name "sqrt A (should all be same)"
  :precision binary64
  (sqrt (+ (* x x) (* x x))))