Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A

Percentage Accurate: 69.1% → 95.2%
Time: 8.9s
Alternatives: 9
Speedup: 1.1×

Specification

?
\[\begin{array}{l} \\ \frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2} \end{array} \]
(FPCore (x y z)
 :precision binary64
 (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))
double code(double x, double y, double z) {
	return (((x * x) + (y * y)) - (z * z)) / (y * 2.0);
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((x * x) + (y * y)) - (z * z)) / (y * 2.0d0)
end function

public static double code(double x, double y, double z) {
	return (((x * x) + (y * y)) - (z * z)) / (y * 2.0);
}

def code(x, y, z):
	return (((x * x) + (y * y)) - (z * z)) / (y * 2.0)

function code(x, y, z)
	return Float64(Float64(Float64(Float64(x * x) + Float64(y * y)) - Float64(z * z)) / Float64(y * 2.0))
end

function tmp = code(x, y, z)
	tmp = (((x * x) + (y * y)) - (z * z)) / (y * 2.0);
end

code[x_, y_, z_] := N[(N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(z * z), $MachinePrecision]), $MachinePrecision] / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 9 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 69.1% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2} \end{array} \]
(FPCore (x y z)
 :precision binary64
 (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))
double code(double x, double y, double z) {
	return (((x * x) + (y * y)) - (z * z)) / (y * 2.0);
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((x * x) + (y * y)) - (z * z)) / (y * 2.0d0)
end function

public static double code(double x, double y, double z) {
	return (((x * x) + (y * y)) - (z * z)) / (y * 2.0);
}

def code(x, y, z):
	return (((x * x) + (y * y)) - (z * z)) / (y * 2.0)

function code(x, y, z)
	return Float64(Float64(Float64(Float64(x * x) + Float64(y * y)) - Float64(z * z)) / Float64(y * 2.0))
end

function tmp = code(x, y, z)
	tmp = (((x * x) + (y * y)) - (z * z)) / (y * 2.0);
end

code[x_, y_, z_] := N[(N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(z * z), $MachinePrecision]), $MachinePrecision] / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
\end{array}

Alternative 1: 95.2% accurate, 0.1× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y_m - z, y_m + z, x \cdot x\right)}{y_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y_m + z}{\frac{y_m}{y_m - z}} + 0.5 \cdot \left(x \cdot \frac{x}{y_m}\right)\\ \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= y_m 5e-37)
    (/ (fma (- y_m z) (+ y_m z) (* x x)) (* y_m 2.0))
    (+ (* 0.5 (/ (+ y_m z) (/ y_m (- y_m z)))) (* 0.5 (* x (/ x y_m)))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (y_m <= 5e-37) {
		tmp = fma((y_m - z), (y_m + z), (x * x)) / (y_m * 2.0);
	} else {
		tmp = (0.5 * ((y_m + z) / (y_m / (y_m - z)))) + (0.5 * (x * (x / y_m)));
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (y_m <= 5e-37)
		tmp = Float64(fma(Float64(y_m - z), Float64(y_m + z), Float64(x * x)) / Float64(y_m * 2.0));
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(y_m + z) / Float64(y_m / Float64(y_m - z)))) + Float64(0.5 * Float64(x * Float64(x / y_m))));
	end
	return Float64(y_s * tmp)
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[y$95$m, 5e-37], N[(N[(N[(y$95$m - z), $MachinePrecision] * N[(y$95$m + z), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(N[(y$95$m + z), $MachinePrecision] / N[(y$95$m / N[(y$95$m - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;y_m \leq 5 \cdot 10^{-37}:\\
\;\;\;\;\frac{\mathsf{fma}\left(y_m - z, y_m + z, x \cdot x\right)}{y_m \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;0.5 \cdot \frac{y_m + z}{\frac{y_m}{y_m - z}} + 0.5 \cdot \left(x \cdot \frac{x}{y_m}\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 2: 96.1% accurate, 0.3× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2}\\ y_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;0.5 \cdot \left(\left(y_m + z\right) \cdot \frac{y_m - z}{y_m}\right)\\ \mathbf{elif}\;t_0 \leq \infty:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{x}{y_m}\right) + y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y_m + z}{\frac{y_m \cdot 2}{y_m - z}}\\ \end{array} \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (/ (- (+ (* x x) (* y_m y_m)) (* z z)) (* y_m 2.0))))
   (*
    y_s
    (if (<= t_0 0.0)
      (* 0.5 (* (+ y_m z) (/ (- y_m z) y_m)))
      (if (<= t_0 INFINITY)
        (+ (* 0.5 (* x (/ x y_m))) (* y_m 0.5))
        (/ (+ y_m z) (/ (* y_m 2.0) (- y_m z))))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double t_0 = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m));
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = (0.5 * (x * (x / y_m))) + (y_m * 0.5);
	} else {
		tmp = (y_m + z) / ((y_m * 2.0) / (y_m - z));
	}
	return y_s * tmp;
}

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double t_0 = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m));
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = (0.5 * (x * (x / y_m))) + (y_m * 0.5);
	} else {
		tmp = (y_m + z) / ((y_m * 2.0) / (y_m - z));
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	t_0 = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)
	tmp = 0
	if t_0 <= 0.0:
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m))
	elif t_0 <= math.inf:
		tmp = (0.5 * (x * (x / y_m))) + (y_m * 0.5)
	else:
		tmp = (y_m + z) / ((y_m * 2.0) / (y_m - z))
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	t_0 = Float64(Float64(Float64(Float64(x * x) + Float64(y_m * y_m)) - Float64(z * z)) / Float64(y_m * 2.0))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(0.5 * Float64(Float64(y_m + z) * Float64(Float64(y_m - z) / y_m)));
	elseif (t_0 <= Inf)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(x / y_m))) + Float64(y_m * 0.5));
	else
		tmp = Float64(Float64(y_m + z) / Float64(Float64(y_m * 2.0) / Float64(y_m - z)));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	t_0 = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m));
	elseif (t_0 <= Inf)
		tmp = (0.5 * (x * (x / y_m))) + (y_m * 0.5);
	else
		tmp = (y_m + z) / ((y_m * 2.0) / (y_m - z));
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x * x), $MachinePrecision] + N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision] - N[(z * z), $MachinePrecision]), $MachinePrecision] / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * If[LessEqual[t$95$0, 0.0], N[(0.5 * N[(N[(y$95$m + z), $MachinePrecision] * N[(N[(y$95$m - z), $MachinePrecision] / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, Infinity], N[(N[(0.5 * N[(x * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y$95$m * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(y$95$m + z), $MachinePrecision] / N[(N[(y$95$m * 2.0), $MachinePrecision] / N[(y$95$m - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
\begin{array}{l}
t_0 := \frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2}\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;t_0 \leq 0:\\
\;\;\;\;0.5 \cdot \left(\left(y_m + z\right) \cdot \frac{y_m - z}{y_m}\right)\\

\mathbf{elif}\;t_0 \leq \infty:\\
\;\;\;\;0.5 \cdot \left(x \cdot \frac{x}{y_m}\right) + y_m \cdot 0.5\\

\mathbf{else}:\\
\;\;\;\;\frac{y_m + z}{\frac{y_m \cdot 2}{y_m - z}}\\


\end{array}
\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 3: 91.6% accurate, 0.7× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := 0.5 \cdot \left(x \cdot \frac{x}{y_m}\right)\\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{+95}:\\ \;\;\;\;0.5 \cdot \frac{y_m + z}{\frac{y_m}{y_m - z}} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + y_m \cdot 0.5\\ \end{array} \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (* 0.5 (* x (/ x y_m)))))
   (*
    y_s
    (if (<= (* x x) 2e+95)
      (+ (* 0.5 (/ (+ y_m z) (/ y_m (- y_m z)))) t_0)
      (+ t_0 (* y_m 0.5))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double t_0 = 0.5 * (x * (x / y_m));
	double tmp;
	if ((x * x) <= 2e+95) {
		tmp = (0.5 * ((y_m + z) / (y_m / (y_m - z)))) + t_0;
	} else {
		tmp = t_0 + (y_m * 0.5);
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (x * (x / y_m))
    if ((x * x) <= 2d+95) then
        tmp = (0.5d0 * ((y_m + z) / (y_m / (y_m - z)))) + t_0
    else
        tmp = t_0 + (y_m * 0.5d0)
    end if
    code = y_s * tmp
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double t_0 = 0.5 * (x * (x / y_m));
	double tmp;
	if ((x * x) <= 2e+95) {
		tmp = (0.5 * ((y_m + z) / (y_m / (y_m - z)))) + t_0;
	} else {
		tmp = t_0 + (y_m * 0.5);
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	t_0 = 0.5 * (x * (x / y_m))
	tmp = 0
	if (x * x) <= 2e+95:
		tmp = (0.5 * ((y_m + z) / (y_m / (y_m - z)))) + t_0
	else:
		tmp = t_0 + (y_m * 0.5)
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	t_0 = Float64(0.5 * Float64(x * Float64(x / y_m)))
	tmp = 0.0
	if (Float64(x * x) <= 2e+95)
		tmp = Float64(Float64(0.5 * Float64(Float64(y_m + z) / Float64(y_m / Float64(y_m - z)))) + t_0);
	else
		tmp = Float64(t_0 + Float64(y_m * 0.5));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	t_0 = 0.5 * (x * (x / y_m));
	tmp = 0.0;
	if ((x * x) <= 2e+95)
		tmp = (0.5 * ((y_m + z) / (y_m / (y_m - z)))) + t_0;
	else
		tmp = t_0 + (y_m * 0.5);
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := Block[{t$95$0 = N[(0.5 * N[(x * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * If[LessEqual[N[(x * x), $MachinePrecision], 2e+95], N[(N[(0.5 * N[(N[(y$95$m + z), $MachinePrecision] / N[(y$95$m / N[(y$95$m - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(y$95$m * 0.5), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
\begin{array}{l}
t_0 := 0.5 \cdot \left(x \cdot \frac{x}{y_m}\right)\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;x \cdot x \leq 2 \cdot 10^{+95}:\\
\;\;\;\;0.5 \cdot \frac{y_m + z}{\frac{y_m}{y_m - z}} + t_0\\

\mathbf{else}:\\
\;\;\;\;t_0 + y_m \cdot 0.5\\


\end{array}
\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 4: 41.6% accurate, 1.1× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{-72} \lor \neg \left(x \leq 1.4 \cdot 10^{+77}\right) \land x \leq 2.9 \cdot 10^{+106}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (or (<= x 7.8e-72) (and (not (<= x 1.4e+77)) (<= x 2.9e+106)))
    (* y_m 0.5)
    (* (/ x y_m) (/ x 2.0)))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if ((x <= 7.8e-72) || (!(x <= 1.4e+77) && (x <= 2.9e+106))) {
		tmp = y_m * 0.5;
	} else {
		tmp = (x / y_m) * (x / 2.0);
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= 7.8d-72) .or. (.not. (x <= 1.4d+77)) .and. (x <= 2.9d+106)) then
        tmp = y_m * 0.5d0
    else
        tmp = (x / y_m) * (x / 2.0d0)
    end if
    code = y_s * tmp
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if ((x <= 7.8e-72) || (!(x <= 1.4e+77) && (x <= 2.9e+106))) {
		tmp = y_m * 0.5;
	} else {
		tmp = (x / y_m) * (x / 2.0);
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if (x <= 7.8e-72) or (not (x <= 1.4e+77) and (x <= 2.9e+106)):
		tmp = y_m * 0.5
	else:
		tmp = (x / y_m) * (x / 2.0)
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if ((x <= 7.8e-72) || (!(x <= 1.4e+77) && (x <= 2.9e+106)))
		tmp = Float64(y_m * 0.5);
	else
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if ((x <= 7.8e-72) || (~((x <= 1.4e+77)) && (x <= 2.9e+106)))
		tmp = y_m * 0.5;
	else
		tmp = (x / y_m) * (x / 2.0);
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[Or[LessEqual[x, 7.8e-72], And[N[Not[LessEqual[x, 1.4e+77]], $MachinePrecision], LessEqual[x, 2.9e+106]]], N[(y$95$m * 0.5), $MachinePrecision], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;x \leq 7.8 \cdot 10^{-72} \lor \neg \left(x \leq 1.4 \cdot 10^{+77}\right) \land x \leq 2.9 \cdot 10^{+106}:\\
\;\;\;\;y_m \cdot 0.5\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 5: 41.6% accurate, 1.1× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{-72}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+106}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y_m \cdot \frac{2}{x}}\\ \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= x 7.8e-72)
    (* y_m 0.5)
    (if (<= x 2.6e+80)
      (* (/ x y_m) (/ x 2.0))
      (if (<= x 3.6e+106) (* y_m 0.5) (/ x (* y_m (/ 2.0 x))))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 7.8e-72) {
		tmp = y_m * 0.5;
	} else if (x <= 2.6e+80) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 3.6e+106) {
		tmp = y_m * 0.5;
	} else {
		tmp = x / (y_m * (2.0 / x));
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 7.8d-72) then
        tmp = y_m * 0.5d0
    else if (x <= 2.6d+80) then
        tmp = (x / y_m) * (x / 2.0d0)
    else if (x <= 3.6d+106) then
        tmp = y_m * 0.5d0
    else
        tmp = x / (y_m * (2.0d0 / x))
    end if
    code = y_s * tmp
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 7.8e-72) {
		tmp = y_m * 0.5;
	} else if (x <= 2.6e+80) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 3.6e+106) {
		tmp = y_m * 0.5;
	} else {
		tmp = x / (y_m * (2.0 / x));
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if x <= 7.8e-72:
		tmp = y_m * 0.5
	elif x <= 2.6e+80:
		tmp = (x / y_m) * (x / 2.0)
	elif x <= 3.6e+106:
		tmp = y_m * 0.5
	else:
		tmp = x / (y_m * (2.0 / x))
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (x <= 7.8e-72)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 2.6e+80)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	elseif (x <= 3.6e+106)
		tmp = Float64(y_m * 0.5);
	else
		tmp = Float64(x / Float64(y_m * Float64(2.0 / x)));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (x <= 7.8e-72)
		tmp = y_m * 0.5;
	elseif (x <= 2.6e+80)
		tmp = (x / y_m) * (x / 2.0);
	elseif (x <= 3.6e+106)
		tmp = y_m * 0.5;
	else
		tmp = x / (y_m * (2.0 / x));
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[x, 7.8e-72], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 2.6e+80], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+106], N[(y$95$m * 0.5), $MachinePrecision], N[(x / N[(y$95$m * N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;x \leq 7.8 \cdot 10^{-72}:\\
\;\;\;\;y_m \cdot 0.5\\

\mathbf{elif}\;x \leq 2.6 \cdot 10^{+80}:\\
\;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\

\mathbf{elif}\;x \leq 3.6 \cdot 10^{+106}:\\
\;\;\;\;y_m \cdot 0.5\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y_m \cdot \frac{2}{x}}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 6: 41.7% accurate, 1.1× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{-72}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+78}:\\ \;\;\;\;\frac{x \cdot \left(-x\right)}{y_m \cdot -2}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+106}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y_m \cdot \frac{2}{x}}\\ \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= x 7.2e-72)
    (* y_m 0.5)
    (if (<= x 3.05e+78)
      (/ (* x (- x)) (* y_m -2.0))
      (if (<= x 3.2e+106) (* y_m 0.5) (/ x (* y_m (/ 2.0 x))))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 7.2e-72) {
		tmp = y_m * 0.5;
	} else if (x <= 3.05e+78) {
		tmp = (x * -x) / (y_m * -2.0);
	} else if (x <= 3.2e+106) {
		tmp = y_m * 0.5;
	} else {
		tmp = x / (y_m * (2.0 / x));
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 7.2d-72) then
        tmp = y_m * 0.5d0
    else if (x <= 3.05d+78) then
        tmp = (x * -x) / (y_m * (-2.0d0))
    else if (x <= 3.2d+106) then
        tmp = y_m * 0.5d0
    else
        tmp = x / (y_m * (2.0d0 / x))
    end if
    code = y_s * tmp
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 7.2e-72) {
		tmp = y_m * 0.5;
	} else if (x <= 3.05e+78) {
		tmp = (x * -x) / (y_m * -2.0);
	} else if (x <= 3.2e+106) {
		tmp = y_m * 0.5;
	} else {
		tmp = x / (y_m * (2.0 / x));
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if x <= 7.2e-72:
		tmp = y_m * 0.5
	elif x <= 3.05e+78:
		tmp = (x * -x) / (y_m * -2.0)
	elif x <= 3.2e+106:
		tmp = y_m * 0.5
	else:
		tmp = x / (y_m * (2.0 / x))
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (x <= 7.2e-72)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 3.05e+78)
		tmp = Float64(Float64(x * Float64(-x)) / Float64(y_m * -2.0));
	elseif (x <= 3.2e+106)
		tmp = Float64(y_m * 0.5);
	else
		tmp = Float64(x / Float64(y_m * Float64(2.0 / x)));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (x <= 7.2e-72)
		tmp = y_m * 0.5;
	elseif (x <= 3.05e+78)
		tmp = (x * -x) / (y_m * -2.0);
	elseif (x <= 3.2e+106)
		tmp = y_m * 0.5;
	else
		tmp = x / (y_m * (2.0 / x));
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[x, 7.2e-72], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 3.05e+78], N[(N[(x * (-x)), $MachinePrecision] / N[(y$95$m * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+106], N[(y$95$m * 0.5), $MachinePrecision], N[(x / N[(y$95$m * N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;x \leq 7.2 \cdot 10^{-72}:\\
\;\;\;\;y_m \cdot 0.5\\

\mathbf{elif}\;x \leq 3.05 \cdot 10^{+78}:\\
\;\;\;\;\frac{x \cdot \left(-x\right)}{y_m \cdot -2}\\

\mathbf{elif}\;x \leq 3.2 \cdot 10^{+106}:\\
\;\;\;\;y_m \cdot 0.5\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y_m \cdot \frac{2}{x}}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 7: 74.0% accurate, 1.1× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(\left(y_m + z\right) \cdot \frac{y_m - z}{y_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y_m \cdot \frac{2}{x}}\\ \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= x 3.1e+106)
    (* 0.5 (* (+ y_m z) (/ (- y_m z) y_m)))
    (/ x (* y_m (/ 2.0 x))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 3.1e+106) {
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m));
	} else {
		tmp = x / (y_m * (2.0 / x));
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 3.1d+106) then
        tmp = 0.5d0 * ((y_m + z) * ((y_m - z) / y_m))
    else
        tmp = x / (y_m * (2.0d0 / x))
    end if
    code = y_s * tmp
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 3.1e+106) {
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m));
	} else {
		tmp = x / (y_m * (2.0 / x));
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if x <= 3.1e+106:
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m))
	else:
		tmp = x / (y_m * (2.0 / x))
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (x <= 3.1e+106)
		tmp = Float64(0.5 * Float64(Float64(y_m + z) * Float64(Float64(y_m - z) / y_m)));
	else
		tmp = Float64(x / Float64(y_m * Float64(2.0 / x)));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (x <= 3.1e+106)
		tmp = 0.5 * ((y_m + z) * ((y_m - z) / y_m));
	else
		tmp = x / (y_m * (2.0 / x));
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[x, 3.1e+106], N[(0.5 * N[(N[(y$95$m + z), $MachinePrecision] * N[(N[(y$95$m - z), $MachinePrecision] / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y$95$m * N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;x \leq 3.1 \cdot 10^{+106}:\\
\;\;\;\;0.5 \cdot \left(\left(y_m + z\right) \cdot \frac{y_m - z}{y_m}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y_m \cdot \frac{2}{x}}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 8: 34.9% accurate, 1.7× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y_m \cdot -2}\\ \end{array} \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (* y_s (if (<= z 8.5e+175) (* y_m 0.5) (* x (/ x (* y_m -2.0))))))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (z <= 8.5e+175) {
		tmp = y_m * 0.5;
	} else {
		tmp = x * (x / (y_m * -2.0));
	}
	return y_s * tmp;
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 8.5d+175) then
        tmp = y_m * 0.5d0
    else
        tmp = x * (x / (y_m * (-2.0d0)))
    end if
    code = y_s * tmp
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (z <= 8.5e+175) {
		tmp = y_m * 0.5;
	} else {
		tmp = x * (x / (y_m * -2.0));
	}
	return y_s * tmp;
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if z <= 8.5e+175:
		tmp = y_m * 0.5
	else:
		tmp = x * (x / (y_m * -2.0))
	return y_s * tmp

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (z <= 8.5e+175)
		tmp = Float64(y_m * 0.5);
	else
		tmp = Float64(x * Float64(x / Float64(y_m * -2.0)));
	end
	return Float64(y_s * tmp)
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (z <= 8.5e+175)
		tmp = y_m * 0.5;
	else
		tmp = x * (x / (y_m * -2.0));
	end
	tmp_2 = y_s * tmp;
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[z, 8.5e+175], N[(y$95$m * 0.5), $MachinePrecision], N[(x * N[(x / N[(y$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \begin{array}{l}
\mathbf{if}\;z \leq 8.5 \cdot 10^{+175}:\\
\;\;\;\;y_m \cdot 0.5\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{x}{y_m \cdot -2}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 9: 34.3% accurate, 5.0× speedup?

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(y_m \cdot 0.5\right) \end{array} \]
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z) :precision binary64 (* y_s (* y_m 0.5)))
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	return y_s * (y_m * 0.5);
}

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = y_s * (y_m * 0.5d0)
end function

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	return y_s * (y_m * 0.5);
}

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	return y_s * (y_m * 0.5)

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	return Float64(y_s * Float64(y_m * 0.5))
end

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp = code(y_s, x, y_m, z)
	tmp = y_s * (y_m * 0.5);
end

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * N[(y$95$m * 0.5), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}
y_m = \left|y\right|
\\
y_s = \mathsf{copysign}\left(1, y\right)

\\
y_s \cdot \left(y_m \cdot 0.5\right)
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup?

\[\begin{array}{l} \\ y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right) \end{array} \]
(FPCore (x y z)
 :precision binary64
 (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x))))
double code(double x, double y, double z) {
	return (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x));
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y * 0.5d0) - (((0.5d0 / y) * (z + x)) * (z - x))
end function

public static double code(double x, double y, double z) {
	return (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x));
}

def code(x, y, z):
	return (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x))

function code(x, y, z)
	return Float64(Float64(y * 0.5) - Float64(Float64(Float64(0.5 / y) * Float64(z + x)) * Float64(z - x)))
end

function tmp = code(x, y, z)
	tmp = (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x));
end

code[x_, y_, z_] := N[(N[(y * 0.5), $MachinePrecision] - N[(N[(N[(0.5 / y), $MachinePrecision] * N[(z + x), $MachinePrecision]), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)
\end{array}

Reproduce

?
herbie shell --seed 2024008 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))