Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3

Percentage Accurate: 50.9% → 79.1%

Time: 8.0s

Alternatives: 3

Speedup: 4.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot 4\right) \cdot y\\ \frac{x \cdot x - t\_0}{x \cdot x + t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y 4.0) y))) (/ (- (* x x) t_0) (+ (* x x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = (y * 4.0d0) * y
    code = ((x * x) - t_0) / ((x * x) + t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + t_0);
}

Python

def code(x, y):
	t_0 = (y * 4.0) * y
	return ((x * x) - t_0) / ((x * x) + t_0)

Julia

function code(x, y)
	t_0 = Float64(Float64(y * 4.0) * y)
	return Float64(Float64(Float64(x * x) - t_0) / Float64(Float64(x * x) + t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = (y * 4.0) * y;
	tmp = ((x * x) - t_0) / ((x * x) + t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * 4.0), $MachinePrecision] * y), $MachinePrecision]}, N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]

Initial Program: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot 4\right) \cdot y\\ \frac{x \cdot x - t\_0}{x \cdot x + t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y 4.0) y))) (/ (- (* x x) t_0) (+ (* x x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = (y * 4.0d0) * y
    code = ((x * x) - t_0) / ((x * x) + t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + t_0);
}

Python

def code(x, y):
	t_0 = (y * 4.0) * y
	return ((x * x) - t_0) / ((x * x) + t_0)

Julia

function code(x, y)
	t_0 = Float64(Float64(y * 4.0) * y)
	return Float64(Float64(Float64(x * x) - t_0) / Float64(Float64(x * x) + t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = (y * 4.0) * y;
	tmp = ((x * x) - t_0) / ((x * x) + t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * 4.0), $MachinePrecision] * y), $MachinePrecision]}, N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.2 \cdot 10^{-167}:\\ \;\;\;\;1\\ \mathbf{elif}\;y\_m \leq 2.16 \cdot 10^{+83}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, \left(y\_m \cdot y\_m\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \left(y\_m \cdot y\_m\right) \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{x}{y\_m \cdot y\_m} \cdot 0.5, -1\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m)
 :precision binary64
 (if (<= y_m 1.2e-167)
   1.0
   (if (<= y_m 2.16e+83)
     (/ (fma x x (* (* y_m y_m) -4.0)) (fma x x (* (* y_m y_m) 4.0)))
     (fma x (* (/ x (* y_m y_m)) 0.5) -1.0))))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double tmp;
	if (y_m <= 1.2e-167) {
		tmp = 1.0;
	} else if (y_m <= 2.16e+83) {
		tmp = fma(x, x, ((y_m * y_m) * -4.0)) / fma(x, x, ((y_m * y_m) * 4.0));
	} else {
		tmp = fma(x, ((x / (y_m * y_m)) * 0.5), -1.0);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m)
	tmp = 0.0
	if (y_m <= 1.2e-167)
		tmp = 1.0;
	elseif (y_m <= 2.16e+83)
		tmp = Float64(fma(x, x, Float64(Float64(y_m * y_m) * -4.0)) / fma(x, x, Float64(Float64(y_m * y_m) * 4.0)));
	else
		tmp = fma(x, Float64(Float64(x / Float64(y_m * y_m)) * 0.5), -1.0);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := If[LessEqual[y$95$m, 1.2e-167], 1.0, If[LessEqual[y$95$m, 2.16e+83], N[(N[(x * x + N[(N[(y$95$m * y$95$m), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / N[(x * x + N[(N[(y$95$m * y$95$m), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.19999999999999997e-167

   1. Initial program 51.7%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 58.4%

      \[\leadsto \color{blue}{1} \]

   if 1.19999999999999997e-167 < y < 2.1599999999999999e83

   1. Initial program 83.6%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{{x}^{2} - 4 \cdot {y}^{2}}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{{x}^{2} + \left(\mathsf{neg}\left(4\right)\right) \cdot {y}^{2}}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      2. unpow2 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x} + \left(\mathsf{neg}\left(4\right)\right) \cdot {y}^{2}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      3. metadata-eval N/A

         \[\leadsto \frac{x \cdot x + \color{blue}{-4} \cdot {y}^{2}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4 \cdot {y}^{2}\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \color{blue}{{y}^{2} \cdot -4}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \color{blue}{{y}^{2} \cdot -4}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      7. unpow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right)} \cdot -4\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

      8. lower-*.f64 82.0

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right)} \cdot -4\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

   5. Simplified 82.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{4 \cdot {y}^{2} + {x}^{2}}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{{x}^{2} + 4 \cdot {y}^{2}}} \]

      2. unpow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{x \cdot x} + 4 \cdot {y}^{2}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{\mathsf{fma}\left(x, x, 4 \cdot {y}^{2}\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \color{blue}{{y}^{2} \cdot 4}\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \color{blue}{{y}^{2} \cdot 4}\right)} \]

      6. unpow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right)} \cdot 4\right)} \]

      7. lower-*.f64 83.6

         \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right)} \cdot 4\right)} \]

   8. Simplified 83.6%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot 4\right)}} \]

   if 2.1599999999999999e83 < y

   1. Initial program 19.6%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{x}^{2}}{{y}^{2}} - 1} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{x}^{2}}{{y}^{2}} + \left(\mathsf{neg}\left(1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot \frac{1}{2}} + \left(\mathsf{neg}\left(1\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x}}{{y}^{2}} \cdot \frac{1}{2} + \left(\mathsf{neg}\left(1\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{{y}^{2}}\right)} \cdot \frac{1}{2} + \left(\mathsf{neg}\left(1\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{{y}^{2}} \cdot \frac{1}{2}\right)} + \left(\mathsf{neg}\left(1\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{x}{{y}^{2}} \cdot \frac{1}{2}, \mathsf{neg}\left(1\right)\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{x}{{y}^{2}} \cdot \frac{1}{2}}, \mathsf{neg}\left(1\right)\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{x}{{y}^{2}}} \cdot \frac{1}{2}, \mathsf{neg}\left(1\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(x, \frac{x}{\color{blue}{y \cdot y}} \cdot \frac{1}{2}, \mathsf{neg}\left(1\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \frac{x}{\color{blue}{y \cdot y}} \cdot \frac{1}{2}, \mathsf{neg}\left(1\right)\right) \]

      11. metadata-eval 88.5

          \[\leadsto \mathsf{fma}\left(x, \frac{x}{y \cdot y} \cdot 0.5, \color{blue}{-1}\right) \]

   5. Simplified 88.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{x}{y \cdot y} \cdot 0.5, -1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 74.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{-62}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 (if (<= (* x x) 1e-62) -1.0 1.0))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double tmp;
	if ((x * x) <= 1e-62) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8) :: tmp
    if ((x * x) <= 1d-62) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	double tmp;
	if ((x * x) <= 1e-62) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	tmp = 0
	if (x * x) <= 1e-62:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

y_m = abs(y)
function code(x, y_m)
	tmp = 0.0
	if (Float64(x * x) <= 1e-62)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m)
	tmp = 0.0;
	if ((x * x) <= 1e-62)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := If[LessEqual[N[(x * x), $MachinePrecision], 1e-62], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1e-62

   1. Initial program 62.5%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 84.4%

      \[\leadsto \color{blue}{-1} \]

   if 1e-62 < (*.f64 x x)

   1. Initial program 45.6%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 75.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 49.0% accurate, 48.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ -1 \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 -1.0)

C

y_m = fabs(y);
double code(double x, double y_m) {
	return -1.0;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    code = -1.0d0
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	return -1.0;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	return -1.0

Julia

y_m = abs(y)
function code(x, y_m)
	return -1.0
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m)
	tmp = -1.0;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := -1.0

Derivation

1. Initial program 53.5%

   \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Simplified 52.6%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 1: 51.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot y\right) \cdot 4\\ t_1 := x \cdot x + t\_0\\ t_2 := \frac{t\_0}{t\_1}\\ t_3 := \left(y \cdot 4\right) \cdot y\\ \mathbf{if}\;\frac{x \cdot x - t\_3}{x \cdot x + t\_3} < 0.9743233849626781:\\ \;\;\;\;\frac{x \cdot x}{t\_1} - t\_2\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\sqrt{t\_1}}\right)}^{2} - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y y) 4.0))
        (t_1 (+ (* x x) t_0))
        (t_2 (/ t_0 t_1))
        (t_3 (* (* y 4.0) y)))
   (if (< (/ (- (* x x) t_3) (+ (* x x) t_3)) 0.9743233849626781)
     (- (/ (* x x) t_1) t_2)
     (- (pow (/ x (sqrt t_1)) 2.0) t_2))))

C

double code(double x, double y) {
	double t_0 = (y * y) * 4.0;
	double t_1 = (x * x) + t_0;
	double t_2 = t_0 / t_1;
	double t_3 = (y * 4.0) * y;
	double tmp;
	if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781) {
		tmp = ((x * x) / t_1) - t_2;
	} else {
		tmp = pow((x / sqrt(t_1)), 2.0) - t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (y * y) * 4.0d0
    t_1 = (x * x) + t_0
    t_2 = t_0 / t_1
    t_3 = (y * 4.0d0) * y
    if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781d0) then
        tmp = ((x * x) / t_1) - t_2
    else
        tmp = ((x / sqrt(t_1)) ** 2.0d0) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * y) * 4.0;
	double t_1 = (x * x) + t_0;
	double t_2 = t_0 / t_1;
	double t_3 = (y * 4.0) * y;
	double tmp;
	if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781) {
		tmp = ((x * x) / t_1) - t_2;
	} else {
		tmp = Math.pow((x / Math.sqrt(t_1)), 2.0) - t_2;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * y) * 4.0
	t_1 = (x * x) + t_0
	t_2 = t_0 / t_1
	t_3 = (y * 4.0) * y
	tmp = 0
	if (((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781:
		tmp = ((x * x) / t_1) - t_2
	else:
		tmp = math.pow((x / math.sqrt(t_1)), 2.0) - t_2
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * y) * 4.0)
	t_1 = Float64(Float64(x * x) + t_0)
	t_2 = Float64(t_0 / t_1)
	t_3 = Float64(Float64(y * 4.0) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(x * x) - t_3) / Float64(Float64(x * x) + t_3)) < 0.9743233849626781)
		tmp = Float64(Float64(Float64(x * x) / t_1) - t_2);
	else
		tmp = Float64((Float64(x / sqrt(t_1)) ^ 2.0) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * y) * 4.0;
	t_1 = (x * x) + t_0;
	t_2 = t_0 / t_1;
	t_3 = (y * 4.0) * y;
	tmp = 0.0;
	if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781)
		tmp = ((x * x) / t_1) - t_2;
	else
		tmp = ((x / sqrt(t_1)) ^ 2.0) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * 4.0), $MachinePrecision] * y), $MachinePrecision]}, If[Less[N[(N[(N[(x * x), $MachinePrecision] - t$95$3), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], 0.9743233849626781], N[(N[(N[(x * x), $MachinePrecision] / t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[Power[N[(x / N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024215 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 9743233849626781/10000000000000000) (- (/ (* x x) (+ (* x x) (* (* y y) 4))) (/ (* (* y y) 4) (+ (* x x) (* (* y y) 4)))) (- (pow (/ x (sqrt (+ (* x x) (* (* y y) 4)))) 2) (/ (* (* y y) 4) (+ (* x x) (* (* y y) 4))))))

  (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))