Linear.Quaternion:$clog from linear-1.19.1.3

Percentage Accurate: 68.9% → 99.9%

Time: 1.5s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+155}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{x \cdot x + y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+155) (- x) (if (<= x 2e+146) (sqrt (+ (* x x) y)) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+155) {
		tmp = -x;
	} else if (x <= 2e+146) {
		tmp = sqrt(((x * x) + y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1d+155)) then
        tmp = -x
    else if (x <= 2d+146) then
        tmp = sqrt(((x * x) + y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e+155) {
		tmp = -x;
	} else if (x <= 2e+146) {
		tmp = Math.sqrt(((x * x) + y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+155:
		tmp = -x
	elif x <= 2e+146:
		tmp = math.sqrt(((x * x) + y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+155)
		tmp = Float64(-x);
	elseif (x <= 2e+146)
		tmp = sqrt(Float64(Float64(x * x) + y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+155)
		tmp = -x;
	elseif (x <= 2e+146)
		tmp = sqrt(((x * x) + y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+155], (-x), If[LessEqual[x, 2e+146], N[Sqrt[N[(N[(x * x), $MachinePrecision] + y), $MachinePrecision]], $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000001e155

   1. Initial program 6.8%

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

   2. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   if -1.00000000000000001e155 < x < 1.99999999999999987e146

   1. Initial program 100.0%

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

   if 1.99999999999999987e146 < x

   1. Initial program 11.2%

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

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+155}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{x \cdot x + y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{x} \cdot -0.5 - x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-100}:\\ \;\;\;\;\sqrt{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{x} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.6e-46)
   (- (* (/ y x) -0.5) x)
   (if (<= x 6.2e-100) (sqrt y) (+ x (* (/ y x) 0.5)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.6e-46) {
		tmp = ((y / x) * -0.5) - x;
	} else if (x <= 6.2e-100) {
		tmp = sqrt(y);
	} else {
		tmp = x + ((y / x) * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.6d-46)) then
        tmp = ((y / x) * (-0.5d0)) - x
    else if (x <= 6.2d-100) then
        tmp = sqrt(y)
    else
        tmp = x + ((y / x) * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.6e-46) {
		tmp = ((y / x) * -0.5) - x;
	} else if (x <= 6.2e-100) {
		tmp = Math.sqrt(y);
	} else {
		tmp = x + ((y / x) * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.6e-46:
		tmp = ((y / x) * -0.5) - x
	elif x <= 6.2e-100:
		tmp = math.sqrt(y)
	else:
		tmp = x + ((y / x) * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.6e-46)
		tmp = Float64(Float64(Float64(y / x) * -0.5) - x);
	elseif (x <= 6.2e-100)
		tmp = sqrt(y);
	else
		tmp = Float64(x + Float64(Float64(y / x) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.6e-46)
		tmp = ((y / x) * -0.5) - x;
	elseif (x <= 6.2e-100)
		tmp = sqrt(y);
	else
		tmp = x + ((y / x) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.6e-46], N[(N[(N[(y / x), $MachinePrecision] * -0.5), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 6.2e-100], N[Sqrt[y], $MachinePrecision], N[(x + N[(N[(y / x), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6e-46

   1. Initial program 57.7%

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

   2. Taylor expanded in x around -inf 88.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{y}{x} + -1 \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 88.1%

         \[\leadsto -0.5 \cdot \frac{y}{x} + \color{blue}{\left(-x\right)} \]

      2. unsub-neg 88.1%

         \[\leadsto \color{blue}{-0.5 \cdot \frac{y}{x} - x} \]

      3. *-commutative 88.1%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot -0.5} - x \]

   4. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot -0.5 - x} \]

   if -3.6e-46 < x < 6.1999999999999997e-100

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.1%

      \[\leadsto \color{blue}{\sqrt{y}} \]

   if 6.1999999999999997e-100 < x

   1. Initial program 52.9%

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

   2. Taylor expanded in x around inf 91.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{x} + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{x} \cdot -0.5 - x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-100}:\\ \;\;\;\;\sqrt{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{x} \cdot 0.5\\ \end{array} \]

Alternative 3: 68.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{x} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e-310) (- x) (+ x (* (/ y x) 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = -x;
	} else {
		tmp = x + ((y / x) * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5d-310)) then
        tmp = -x
    else
        tmp = x + ((y / x) * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = -x;
	} else {
		tmp = x + ((y / x) * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-310:
		tmp = -x
	else:
		tmp = x + ((y / x) * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-310)
		tmp = Float64(-x);
	else
		tmp = Float64(x + Float64(Float64(y / x) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e-310)
		tmp = -x;
	else
		tmp = x + ((y / x) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-310], (-x), N[(x + N[(N[(y / x), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.999999999999985e-310

   1. Initial program 71.1%

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

   2. Taylor expanded in x around -inf 66.0%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 66.0%

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

   4. Simplified 66.0%

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

   if -4.999999999999985e-310 < x

   1. Initial program 64.5%

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

   2. Taylor expanded in x around inf 71.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{x} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{x} \cdot 0.5\\ \end{array} \]

Alternative 4: 68.4% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{y}{x} \cdot -0.5 - x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{x} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e-310) (- (* (/ y x) -0.5) x) (+ x (* (/ y x) 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = ((y / x) * -0.5) - x;
	} else {
		tmp = x + ((y / x) * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5d-310)) then
        tmp = ((y / x) * (-0.5d0)) - x
    else
        tmp = x + ((y / x) * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = ((y / x) * -0.5) - x;
	} else {
		tmp = x + ((y / x) * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-310:
		tmp = ((y / x) * -0.5) - x
	else:
		tmp = x + ((y / x) * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-310)
		tmp = Float64(Float64(Float64(y / x) * -0.5) - x);
	else
		tmp = Float64(x + Float64(Float64(y / x) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e-310)
		tmp = ((y / x) * -0.5) - x;
	else
		tmp = x + ((y / x) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-310], N[(N[(N[(y / x), $MachinePrecision] * -0.5), $MachinePrecision] - x), $MachinePrecision], N[(x + N[(N[(y / x), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.999999999999985e-310

   1. Initial program 71.1%

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

   2. Taylor expanded in x around -inf 66.2%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{y}{x} + -1 \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 66.2%

         \[\leadsto -0.5 \cdot \frac{y}{x} + \color{blue}{\left(-x\right)} \]

      2. unsub-neg 66.2%

         \[\leadsto \color{blue}{-0.5 \cdot \frac{y}{x} - x} \]

      3. *-commutative 66.2%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot -0.5} - x \]

   4. Simplified 66.2%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot -0.5 - x} \]

   if -4.999999999999985e-310 < x

   1. Initial program 64.5%

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

   2. Taylor expanded in x around inf 71.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{x} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{y}{x} \cdot -0.5 - x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{x} \cdot 0.5\\ \end{array} \]

Alternative 5: 68.0% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -5e-310) (- x) x))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5d-310)) then
        tmp = -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-310:
		tmp = -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-310)
		tmp = Float64(-x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e-310)
		tmp = -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-310], (-x), x]

Derivation

1. Split input into 2 regimes

2. if x < -4.999999999999985e-310

   1. Initial program 71.1%

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

   2. Taylor expanded in x around -inf 66.0%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 66.0%

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

   4. Simplified 66.0%

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

   if -4.999999999999985e-310 < x

   1. Initial program 64.5%

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

   2. Taylor expanded in x around inf 71.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 34.5% accurate, 105.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

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

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 67.8%

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

2. Taylor expanded in x around inf 36.7%

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

3. Final simplification 36.7%

   \[\leadsto x \]

Developer target: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \frac{y}{x} + x\\ \mathbf{if}\;x < -1.5097698010472593 \cdot 10^{+153}:\\ \;\;\;\;-t_0\\ \mathbf{elif}\;x < 5.582399551122541 \cdot 10^{+57}:\\ \;\;\;\;\sqrt{x \cdot x + y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* 0.5 (/ y x)) x)))
   (if (< x -1.5097698010472593e+153)
     (- t_0)
     (if (< x 5.582399551122541e+57) (sqrt (+ (* x x) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = (0.5 * (y / x)) + x;
	double tmp;
	if (x < -1.5097698010472593e+153) {
		tmp = -t_0;
	} else if (x < 5.582399551122541e+57) {
		tmp = sqrt(((x * x) + y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (0.5d0 * (y / x)) + x
    if (x < (-1.5097698010472593d+153)) then
        tmp = -t_0
    else if (x < 5.582399551122541d+57) then
        tmp = sqrt(((x * x) + y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (0.5 * (y / x)) + x;
	double tmp;
	if (x < -1.5097698010472593e+153) {
		tmp = -t_0;
	} else if (x < 5.582399551122541e+57) {
		tmp = Math.sqrt(((x * x) + y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (0.5 * (y / x)) + x
	tmp = 0
	if x < -1.5097698010472593e+153:
		tmp = -t_0
	elif x < 5.582399551122541e+57:
		tmp = math.sqrt(((x * x) + y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(0.5 * Float64(y / x)) + x)
	tmp = 0.0
	if (x < -1.5097698010472593e+153)
		tmp = Float64(-t_0);
	elseif (x < 5.582399551122541e+57)
		tmp = sqrt(Float64(Float64(x * x) + y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (0.5 * (y / x)) + x;
	tmp = 0.0;
	if (x < -1.5097698010472593e+153)
		tmp = -t_0;
	elseif (x < 5.582399551122541e+57)
		tmp = sqrt(((x * x) + y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(0.5 * N[(y / x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[Less[x, -1.5097698010472593e+153], (-t$95$0), If[Less[x, 5.582399551122541e+57], N[Sqrt[N[(N[(x * x), $MachinePrecision] + y), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023175 
(FPCore (x y)
  :name "Linear.Quaternion:$clog from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< x -1.5097698010472593e+153) (- (+ (* 0.5 (/ y x)) x)) (if (< x 5.582399551122541e+57) (sqrt (+ (* x x) y)) (+ (* 0.5 (/ y x)) x)))

  (sqrt (+ (* x x) y)))