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

Percentage Accurate: 68.9% → 92.1%

Time: 13.2s

Alternatives: 9

Speedup: 0.7×

• 41.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 68.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 92.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \mathsf{hypot}\left(\mathsf{hypot}\left(x, y_m\right), z\right)\\ y_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{y_m} \cdot \frac{z}{-2}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{t_0}{y_m \cdot 2}\\ \end{array} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (hypot (hypot x y_m) z)))
   (*
    y_s
    (if (<= (/ (- (+ (* x x) (* y_m y_m)) (* z z)) (* y_m 2.0)) -5e+38)
      (* (/ z y_m) (/ z -2.0))
      (* t_0 (/ t_0 (* y_m 2.0)))))))

C

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 = hypot(hypot(x, y_m), z);
	double tmp;
	if (((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = t_0 * (t_0 / (y_m * 2.0));
	}
	return y_s * tmp;
}

Java

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 = Math.hypot(Math.hypot(x, y_m), z);
	double tmp;
	if (((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = t_0 * (t_0 / (y_m * 2.0));
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	t_0 = math.hypot(math.hypot(x, y_m), z)
	tmp = 0
	if ((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38:
		tmp = (z / y_m) * (z / -2.0)
	else:
		tmp = t_0 * (t_0 / (y_m * 2.0))
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	t_0 = hypot(hypot(x, y_m), z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(x * x) + Float64(y_m * y_m)) - Float64(z * z)) / Float64(y_m * 2.0)) <= -5e+38)
		tmp = Float64(Float64(z / y_m) * Float64(z / -2.0));
	else
		tmp = Float64(t_0 * Float64(t_0 / Float64(y_m * 2.0)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	t_0 = hypot(hypot(x, y_m), z);
	tmp = 0.0;
	if (((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38)
		tmp = (z / y_m) * (z / -2.0);
	else
		tmp = t_0 * (t_0 / (y_m * 2.0));
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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[Sqrt[N[Sqrt[x ^ 2 + y$95$m ^ 2], $MachinePrecision] ^ 2 + z ^ 2], $MachinePrecision]}, N[(y$95$s * If[LessEqual[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], -5e+38], N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$0 / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 92.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \mathsf{hypot}\left(\mathsf{hypot}\left(x, y_m\right), z\right)\\ y_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{y_m} \cdot \frac{z}{-2}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_0 \cdot \frac{0.5}{y_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (hypot (hypot x y_m) z)))
   (*
    y_s
    (if (<= (/ (- (+ (* x x) (* y_m y_m)) (* z z)) (* y_m 2.0)) -5e+38)
      (* (/ z y_m) (/ z -2.0))
      (* t_0 (* t_0 (/ 0.5 y_m)))))))

C

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 = hypot(hypot(x, y_m), z);
	double tmp;
	if (((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = t_0 * (t_0 * (0.5 / y_m));
	}
	return y_s * tmp;
}

Java

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 = Math.hypot(Math.hypot(x, y_m), z);
	double tmp;
	if (((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = t_0 * (t_0 * (0.5 / y_m));
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	t_0 = math.hypot(math.hypot(x, y_m), z)
	tmp = 0
	if ((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38:
		tmp = (z / y_m) * (z / -2.0)
	else:
		tmp = t_0 * (t_0 * (0.5 / y_m))
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	t_0 = hypot(hypot(x, y_m), z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(x * x) + Float64(y_m * y_m)) - Float64(z * z)) / Float64(y_m * 2.0)) <= -5e+38)
		tmp = Float64(Float64(z / y_m) * Float64(z / -2.0));
	else
		tmp = Float64(t_0 * Float64(t_0 * Float64(0.5 / y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	t_0 = hypot(hypot(x, y_m), z);
	tmp = 0.0;
	if (((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38)
		tmp = (z / y_m) * (z / -2.0);
	else
		tmp = t_0 * (t_0 * (0.5 / y_m));
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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[Sqrt[N[Sqrt[x ^ 2 + y$95$m ^ 2], $MachinePrecision] ^ 2 + z ^ 2], $MachinePrecision]}, N[(y$95$s * If[LessEqual[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], -5e+38], N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$0 * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 91.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{y_m} \cdot \frac{z}{-2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\mathsf{hypot}\left(\mathsf{hypot}\left(x, y_m\right), z\right) \cdot \sqrt{\frac{0.5}{y_m}}\right)}^{2}\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= (/ (- (+ (* x x) (* y_m y_m)) (* z z)) (* y_m 2.0)) -5e+38)
    (* (/ z y_m) (/ z -2.0))
    (pow (* (hypot (hypot x y_m) z) (sqrt (/ 0.5 y_m))) 2.0))))

C

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 * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = pow((hypot(hypot(x, y_m), z) * sqrt((0.5 / y_m))), 2.0);
	}
	return y_s * tmp;
}

Java

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 * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = Math.pow((Math.hypot(Math.hypot(x, y_m), z) * Math.sqrt((0.5 / y_m))), 2.0);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if ((((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38:
		tmp = (z / y_m) * (z / -2.0)
	else:
		tmp = math.pow((math.hypot(math.hypot(x, y_m), z) * math.sqrt((0.5 / y_m))), 2.0)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(x * x) + Float64(y_m * y_m)) - Float64(z * z)) / Float64(y_m * 2.0)) <= -5e+38)
		tmp = Float64(Float64(z / y_m) * Float64(z / -2.0));
	else
		tmp = Float64(hypot(hypot(x, y_m), z) * sqrt(Float64(0.5 / y_m))) ^ 2.0;
	end
	return Float64(y_s * tmp)
end

MATLAB

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 * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)) <= -5e+38)
		tmp = (z / y_m) * (z / -2.0);
	else
		tmp = (hypot(hypot(x, y_m), z) * sqrt((0.5 / y_m))) ^ 2.0;
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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[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], -5e+38], N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Sqrt[N[Sqrt[x ^ 2 + y$95$m ^ 2], $MachinePrecision] ^ 2 + z ^ 2], $MachinePrecision] * N[Sqrt[N[(0.5 / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 43.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 2.45 \cdot 10^{-224}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y_m}\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-91}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y_m} \cdot \frac{z}{-2}\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= z 2.45e-224)
    (* y_m 0.5)
    (if (<= z 8.2e-169)
      (* x (* x (/ 0.5 y_m)))
      (if (<= z 1.12e-91)
        (* y_m 0.5)
        (if (<= z 1.9e+36)
          (* (/ x y_m) (/ x 2.0))
          (* (/ z y_m) (/ z -2.0))))))))

C

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 <= 2.45e-224) {
		tmp = y_m * 0.5;
	} else if (z <= 8.2e-169) {
		tmp = x * (x * (0.5 / y_m));
	} else if (z <= 1.12e-91) {
		tmp = y_m * 0.5;
	} else if (z <= 1.9e+36) {
		tmp = (x / y_m) * (x / 2.0);
	} else {
		tmp = (z / y_m) * (z / -2.0);
	}
	return y_s * tmp;
}

Fortran

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 <= 2.45d-224) then
        tmp = y_m * 0.5d0
    else if (z <= 8.2d-169) then
        tmp = x * (x * (0.5d0 / y_m))
    else if (z <= 1.12d-91) then
        tmp = y_m * 0.5d0
    else if (z <= 1.9d+36) then
        tmp = (x / y_m) * (x / 2.0d0)
    else
        tmp = (z / y_m) * (z / (-2.0d0))
    end if
    code = y_s * tmp
end function

Java

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 <= 2.45e-224) {
		tmp = y_m * 0.5;
	} else if (z <= 8.2e-169) {
		tmp = x * (x * (0.5 / y_m));
	} else if (z <= 1.12e-91) {
		tmp = y_m * 0.5;
	} else if (z <= 1.9e+36) {
		tmp = (x / y_m) * (x / 2.0);
	} else {
		tmp = (z / y_m) * (z / -2.0);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if z <= 2.45e-224:
		tmp = y_m * 0.5
	elif z <= 8.2e-169:
		tmp = x * (x * (0.5 / y_m))
	elif z <= 1.12e-91:
		tmp = y_m * 0.5
	elif z <= 1.9e+36:
		tmp = (x / y_m) * (x / 2.0)
	else:
		tmp = (z / y_m) * (z / -2.0)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (z <= 2.45e-224)
		tmp = Float64(y_m * 0.5);
	elseif (z <= 8.2e-169)
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	elseif (z <= 1.12e-91)
		tmp = Float64(y_m * 0.5);
	elseif (z <= 1.9e+36)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	else
		tmp = Float64(Float64(z / y_m) * Float64(z / -2.0));
	end
	return Float64(y_s * tmp)
end

MATLAB

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 <= 2.45e-224)
		tmp = y_m * 0.5;
	elseif (z <= 8.2e-169)
		tmp = x * (x * (0.5 / y_m));
	elseif (z <= 1.12e-91)
		tmp = y_m * 0.5;
	elseif (z <= 1.9e+36)
		tmp = (x / y_m) * (x / 2.0);
	else
		tmp = (z / y_m) * (z / -2.0);
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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, 2.45e-224], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[z, 8.2e-169], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-91], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[z, 1.9e+36], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 43.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3.5 \cdot 10^{-224}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{y_m}{x}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-90}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y_m} \cdot \frac{z}{-2}\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= z 3.5e-224)
    (* y_m 0.5)
    (if (<= z 4.8e-167)
      (/ (* x 0.5) (/ y_m x))
      (if (<= z 1.1e-90)
        (* y_m 0.5)
        (if (<= z 1.26e+33)
          (* (/ x y_m) (/ x 2.0))
          (* (/ z y_m) (/ z -2.0))))))))

C

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 <= 3.5e-224) {
		tmp = y_m * 0.5;
	} else if (z <= 4.8e-167) {
		tmp = (x * 0.5) / (y_m / x);
	} else if (z <= 1.1e-90) {
		tmp = y_m * 0.5;
	} else if (z <= 1.26e+33) {
		tmp = (x / y_m) * (x / 2.0);
	} else {
		tmp = (z / y_m) * (z / -2.0);
	}
	return y_s * tmp;
}

Fortran

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 <= 3.5d-224) then
        tmp = y_m * 0.5d0
    else if (z <= 4.8d-167) then
        tmp = (x * 0.5d0) / (y_m / x)
    else if (z <= 1.1d-90) then
        tmp = y_m * 0.5d0
    else if (z <= 1.26d+33) then
        tmp = (x / y_m) * (x / 2.0d0)
    else
        tmp = (z / y_m) * (z / (-2.0d0))
    end if
    code = y_s * tmp
end function

Java

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 <= 3.5e-224) {
		tmp = y_m * 0.5;
	} else if (z <= 4.8e-167) {
		tmp = (x * 0.5) / (y_m / x);
	} else if (z <= 1.1e-90) {
		tmp = y_m * 0.5;
	} else if (z <= 1.26e+33) {
		tmp = (x / y_m) * (x / 2.0);
	} else {
		tmp = (z / y_m) * (z / -2.0);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if z <= 3.5e-224:
		tmp = y_m * 0.5
	elif z <= 4.8e-167:
		tmp = (x * 0.5) / (y_m / x)
	elif z <= 1.1e-90:
		tmp = y_m * 0.5
	elif z <= 1.26e+33:
		tmp = (x / y_m) * (x / 2.0)
	else:
		tmp = (z / y_m) * (z / -2.0)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (z <= 3.5e-224)
		tmp = Float64(y_m * 0.5);
	elseif (z <= 4.8e-167)
		tmp = Float64(Float64(x * 0.5) / Float64(y_m / x));
	elseif (z <= 1.1e-90)
		tmp = Float64(y_m * 0.5);
	elseif (z <= 1.26e+33)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	else
		tmp = Float64(Float64(z / y_m) * Float64(z / -2.0));
	end
	return Float64(y_s * tmp)
end

MATLAB

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 <= 3.5e-224)
		tmp = y_m * 0.5;
	elseif (z <= 4.8e-167)
		tmp = (x * 0.5) / (y_m / x);
	elseif (z <= 1.1e-90)
		tmp = y_m * 0.5;
	elseif (z <= 1.26e+33)
		tmp = (x / y_m) * (x / 2.0);
	else
		tmp = (z / y_m) * (z / -2.0);
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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, 3.5e-224], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[z, 4.8e-167], N[(N[(x * 0.5), $MachinePrecision] / N[(y$95$m / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-90], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[z, 1.26e+33], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{-68} \lor \neg \left(x \leq 2.9 \cdot 10^{-57}\right) \land x \leq 6.4 \cdot 10^{+47}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y_m}\right)\\ \end{array} \end{array} \]

FPCore

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 1.2e-68) (and (not (<= x 2.9e-57)) (<= x 6.4e+47)))
    (* y_m 0.5)
    (* x (* x (/ 0.5 y_m))))))

C

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 <= 1.2e-68) || (!(x <= 2.9e-57) && (x <= 6.4e+47))) {
		tmp = y_m * 0.5;
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Fortran

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 <= 1.2d-68) .or. (.not. (x <= 2.9d-57)) .and. (x <= 6.4d+47)) then
        tmp = y_m * 0.5d0
    else
        tmp = x * (x * (0.5d0 / y_m))
    end if
    code = y_s * tmp
end function

Java

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 <= 1.2e-68) || (!(x <= 2.9e-57) && (x <= 6.4e+47))) {
		tmp = y_m * 0.5;
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if (x <= 1.2e-68) or (not (x <= 2.9e-57) and (x <= 6.4e+47)):
		tmp = y_m * 0.5
	else:
		tmp = x * (x * (0.5 / y_m))
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if ((x <= 1.2e-68) || (!(x <= 2.9e-57) && (x <= 6.4e+47)))
		tmp = Float64(y_m * 0.5);
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

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 <= 1.2e-68) || (~((x <= 2.9e-57)) && (x <= 6.4e+47)))
		tmp = y_m * 0.5;
	else
		tmp = x * (x * (0.5 / y_m));
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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, 1.2e-68], And[N[Not[LessEqual[x, 2.9e-57]], $MachinePrecision], LessEqual[x, 6.4e+47]]], N[(y$95$m * 0.5), $MachinePrecision], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 43.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{-68}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+48}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y_m}\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= x 1.2e-68)
    (* y_m 0.5)
    (if (<= x 1.7e-57)
      (* (/ x y_m) (/ x 2.0))
      (if (<= x 5.5e+48) (* y_m 0.5) (* x (* x (/ 0.5 y_m))))))))

C

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 <= 1.2e-68) {
		tmp = y_m * 0.5;
	} else if (x <= 1.7e-57) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 5.5e+48) {
		tmp = y_m * 0.5;
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Fortran

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 <= 1.2d-68) then
        tmp = y_m * 0.5d0
    else if (x <= 1.7d-57) then
        tmp = (x / y_m) * (x / 2.0d0)
    else if (x <= 5.5d+48) then
        tmp = y_m * 0.5d0
    else
        tmp = x * (x * (0.5d0 / y_m))
    end if
    code = y_s * tmp
end function

Java

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 <= 1.2e-68) {
		tmp = y_m * 0.5;
	} else if (x <= 1.7e-57) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 5.5e+48) {
		tmp = y_m * 0.5;
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if x <= 1.2e-68:
		tmp = y_m * 0.5
	elif x <= 1.7e-57:
		tmp = (x / y_m) * (x / 2.0)
	elif x <= 5.5e+48:
		tmp = y_m * 0.5
	else:
		tmp = x * (x * (0.5 / y_m))
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (x <= 1.2e-68)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 1.7e-57)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	elseif (x <= 5.5e+48)
		tmp = Float64(y_m * 0.5);
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

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 <= 1.2e-68)
		tmp = y_m * 0.5;
	elseif (x <= 1.7e-57)
		tmp = (x / y_m) * (x / 2.0);
	elseif (x <= 5.5e+48)
		tmp = y_m * 0.5;
	else
		tmp = x * (x * (0.5 / y_m));
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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, 1.2e-68], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 1.7e-57], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+48], N[(y$95$m * 0.5), $MachinePrecision], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 2.16 \cdot 10^{+157}:\\ \;\;\;\;\frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y_m \cdot 0.5\\ \end{array} \end{array} \]

FPCore

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 2.16e+157)
    (/ (- (+ (* x x) (* y_m y_m)) (* z z)) (* y_m 2.0))
    (* y_m 0.5))))

C

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 <= 2.16e+157) {
		tmp = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0);
	} else {
		tmp = y_m * 0.5;
	}
	return y_s * tmp;
}

Fortran

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 (y_m <= 2.16d+157) then
        tmp = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0d0)
    else
        tmp = y_m * 0.5d0
    end if
    code = y_s * tmp
end function

Java

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 (y_m <= 2.16e+157) {
		tmp = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0);
	} else {
		tmp = y_m * 0.5;
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if y_m <= 2.16e+157:
		tmp = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0)
	else:
		tmp = y_m * 0.5
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (y_m <= 2.16e+157)
		tmp = Float64(Float64(Float64(Float64(x * x) + Float64(y_m * y_m)) - Float64(z * z)) / Float64(y_m * 2.0));
	else
		tmp = Float64(y_m * 0.5);
	end
	return Float64(y_s * tmp)
end

MATLAB

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 (y_m <= 2.16e+157)
		tmp = (((x * x) + (y_m * y_m)) - (z * z)) / (y_m * 2.0);
	else
		tmp = y_m * 0.5;
	end
	tmp_2 = y_s * tmp;
end

Wolfram

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, 2.16e+157], 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$95$m * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 34.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(y_m \cdot 0.5\right) \end{array} \]

FPCore

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)))

C

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);
}

Fortran

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

Java

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);
}

Python

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)

Julia

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

MATLAB

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

Wolfram

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]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Reproduce

herbie shell --seed 2024006 
(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)))