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

Percentage Accurate: 69.4% → 88.0%

Time: 16.3s

Alternatives: 8

Speedup: 0.9×

• 41.6% 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: 69.4% 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: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 5.8 \cdot 10^{+159}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y_m - z, y_m + z, x \cdot x\right)}{y_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y_m \cdot 0.5\\ \end{array} \end{array} \]

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 5.8e+159)
    (/ (fma (- y_m z) (+ y_m z) (* x x)) (* 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 <= 5.8e+159) {
		tmp = fma((y_m - z), (y_m + z), (x * x)) / (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 <= 5.8e+159)
		tmp = Float64(fma(Float64(y_m - z), Float64(y_m + z), Float64(x * x)) / Float64(y_m * 2.0));
	else
		tmp = Float64(y_m * 0.5);
	end
	return Float64(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, 5.8e+159], 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[(y$95$m * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 43.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \frac{z}{y_m} \cdot \frac{z}{-2}\\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{-186}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-40}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3200000:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (* (/ z y_m) (/ z -2.0))))
   (*
    y_s
    (if (<= x 1.9e-186)
      (* y_m 0.5)
      (if (<= x 3.8e-94)
        t_0
        (if (<= x 9.5e-40)
          (* y_m 0.5)
          (if (<= x 4.3e-6)
            t_0
            (if (<= x 3200000.0)
              (* (/ x y_m) (/ x 2.0))
              (if (<= x 1.45e+47) t_0 (* 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 t_0 = (z / y_m) * (z / -2.0);
	double tmp;
	if (x <= 1.9e-186) {
		tmp = y_m * 0.5;
	} else if (x <= 3.8e-94) {
		tmp = t_0;
	} else if (x <= 9.5e-40) {
		tmp = y_m * 0.5;
	} else if (x <= 4.3e-6) {
		tmp = t_0;
	} else if (x <= 3200000.0) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 1.45e+47) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (z / y_m) * (z / (-2.0d0))
    if (x <= 1.9d-186) then
        tmp = y_m * 0.5d0
    else if (x <= 3.8d-94) then
        tmp = t_0
    else if (x <= 9.5d-40) then
        tmp = y_m * 0.5d0
    else if (x <= 4.3d-6) then
        tmp = t_0
    else if (x <= 3200000.0d0) then
        tmp = (x / y_m) * (x / 2.0d0)
    else if (x <= 1.45d+47) then
        tmp = t_0
    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 t_0 = (z / y_m) * (z / -2.0);
	double tmp;
	if (x <= 1.9e-186) {
		tmp = y_m * 0.5;
	} else if (x <= 3.8e-94) {
		tmp = t_0;
	} else if (x <= 9.5e-40) {
		tmp = y_m * 0.5;
	} else if (x <= 4.3e-6) {
		tmp = t_0;
	} else if (x <= 3200000.0) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 1.45e+47) {
		tmp = t_0;
	} 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):
	t_0 = (z / y_m) * (z / -2.0)
	tmp = 0
	if x <= 1.9e-186:
		tmp = y_m * 0.5
	elif x <= 3.8e-94:
		tmp = t_0
	elif x <= 9.5e-40:
		tmp = y_m * 0.5
	elif x <= 4.3e-6:
		tmp = t_0
	elif x <= 3200000.0:
		tmp = (x / y_m) * (x / 2.0)
	elif x <= 1.45e+47:
		tmp = t_0
	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)
	t_0 = Float64(Float64(z / y_m) * Float64(z / -2.0))
	tmp = 0.0
	if (x <= 1.9e-186)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 3.8e-94)
		tmp = t_0;
	elseif (x <= 9.5e-40)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 4.3e-6)
		tmp = t_0;
	elseif (x <= 3200000.0)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	elseif (x <= 1.45e+47)
		tmp = t_0;
	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)
	t_0 = (z / y_m) * (z / -2.0);
	tmp = 0.0;
	if (x <= 1.9e-186)
		tmp = y_m * 0.5;
	elseif (x <= 3.8e-94)
		tmp = t_0;
	elseif (x <= 9.5e-40)
		tmp = y_m * 0.5;
	elseif (x <= 4.3e-6)
		tmp = t_0;
	elseif (x <= 3200000.0)
		tmp = (x / y_m) * (x / 2.0);
	elseif (x <= 1.45e+47)
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * If[LessEqual[x, 1.9e-186], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 3.8e-94], t$95$0, If[LessEqual[x, 9.5e-40], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 4.3e-6], t$95$0, If[LessEqual[x, 3200000.0], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+47], t$95$0, N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 3: 43.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \frac{z}{y_m} \cdot \frac{z}{-2}\\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 580000:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{y_m}{x}}\\ \end{array} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (* (/ z y_m) (/ z -2.0))))
   (*
    y_s
    (if (<= x 3.5e-187)
      (* y_m 0.5)
      (if (<= x 3.2e-94)
        t_0
        (if (<= x 8.5e-40)
          (* y_m 0.5)
          (if (<= x 4e-6)
            t_0
            (if (<= x 580000.0)
              (* (/ x y_m) (/ x 2.0))
              (if (<= x 7.6e+47) t_0 (/ (* x 0.5) (/ y_m x)))))))))))

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 = (z / y_m) * (z / -2.0);
	double tmp;
	if (x <= 3.5e-187) {
		tmp = y_m * 0.5;
	} else if (x <= 3.2e-94) {
		tmp = t_0;
	} else if (x <= 8.5e-40) {
		tmp = y_m * 0.5;
	} else if (x <= 4e-6) {
		tmp = t_0;
	} else if (x <= 580000.0) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 7.6e+47) {
		tmp = t_0;
	} else {
		tmp = (x * 0.5) / (y_m / x);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (z / y_m) * (z / (-2.0d0))
    if (x <= 3.5d-187) then
        tmp = y_m * 0.5d0
    else if (x <= 3.2d-94) then
        tmp = t_0
    else if (x <= 8.5d-40) then
        tmp = y_m * 0.5d0
    else if (x <= 4d-6) then
        tmp = t_0
    else if (x <= 580000.0d0) then
        tmp = (x / y_m) * (x / 2.0d0)
    else if (x <= 7.6d+47) then
        tmp = t_0
    else
        tmp = (x * 0.5d0) / (y_m / x)
    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 t_0 = (z / y_m) * (z / -2.0);
	double tmp;
	if (x <= 3.5e-187) {
		tmp = y_m * 0.5;
	} else if (x <= 3.2e-94) {
		tmp = t_0;
	} else if (x <= 8.5e-40) {
		tmp = y_m * 0.5;
	} else if (x <= 4e-6) {
		tmp = t_0;
	} else if (x <= 580000.0) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 7.6e+47) {
		tmp = t_0;
	} else {
		tmp = (x * 0.5) / (y_m / x);
	}
	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 = (z / y_m) * (z / -2.0)
	tmp = 0
	if x <= 3.5e-187:
		tmp = y_m * 0.5
	elif x <= 3.2e-94:
		tmp = t_0
	elif x <= 8.5e-40:
		tmp = y_m * 0.5
	elif x <= 4e-6:
		tmp = t_0
	elif x <= 580000.0:
		tmp = (x / y_m) * (x / 2.0)
	elif x <= 7.6e+47:
		tmp = t_0
	else:
		tmp = (x * 0.5) / (y_m / x)
	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 = Float64(Float64(z / y_m) * Float64(z / -2.0))
	tmp = 0.0
	if (x <= 3.5e-187)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 3.2e-94)
		tmp = t_0;
	elseif (x <= 8.5e-40)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 4e-6)
		tmp = t_0;
	elseif (x <= 580000.0)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	elseif (x <= 7.6e+47)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * 0.5) / Float64(y_m / x));
	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 = (z / y_m) * (z / -2.0);
	tmp = 0.0;
	if (x <= 3.5e-187)
		tmp = y_m * 0.5;
	elseif (x <= 3.2e-94)
		tmp = t_0;
	elseif (x <= 8.5e-40)
		tmp = y_m * 0.5;
	elseif (x <= 4e-6)
		tmp = t_0;
	elseif (x <= 580000.0)
		tmp = (x / y_m) * (x / 2.0);
	elseif (x <= 7.6e+47)
		tmp = t_0;
	else
		tmp = (x * 0.5) / (y_m / x);
	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[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * If[LessEqual[x, 3.5e-187], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 3.2e-94], t$95$0, If[LessEqual[x, 8.5e-40], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 4e-6], t$95$0, If[LessEqual[x, 580000.0], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e+47], t$95$0, N[(N[(x * 0.5), $MachinePrecision] / N[(y$95$m / x), $MachinePrecision]), $MachinePrecision]]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 4: 54.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \frac{\left(y_m - z\right) \cdot \left(y_m + z\right)}{y_m \cdot 2}\\ y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 4.7 \cdot 10^{-242}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-229}:\\ \;\;\;\;y_m \cdot 0.5\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 370000:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{z}{y_m} \cdot \frac{z}{-2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{y_m}{x}}\\ \end{array} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (let* ((t_0 (/ (* (- y_m z) (+ y_m z)) (* y_m 2.0))))
   (*
    y_s
    (if (<= x 4.7e-242)
      t_0
      (if (<= x 1.1e-229)
        (* y_m 0.5)
        (if (<= x 4.6e-6)
          t_0
          (if (<= x 370000.0)
            (* (/ x y_m) (/ x 2.0))
            (if (<= x 7.2e+47)
              (* (/ z y_m) (/ z -2.0))
              (/ (* x 0.5) (/ y_m x))))))))))

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 = ((y_m - z) * (y_m + z)) / (y_m * 2.0);
	double tmp;
	if (x <= 4.7e-242) {
		tmp = t_0;
	} else if (x <= 1.1e-229) {
		tmp = y_m * 0.5;
	} else if (x <= 4.6e-6) {
		tmp = t_0;
	} else if (x <= 370000.0) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 7.2e+47) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = (x * 0.5) / (y_m / x);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = ((y_m - z) * (y_m + z)) / (y_m * 2.0d0)
    if (x <= 4.7d-242) then
        tmp = t_0
    else if (x <= 1.1d-229) then
        tmp = y_m * 0.5d0
    else if (x <= 4.6d-6) then
        tmp = t_0
    else if (x <= 370000.0d0) then
        tmp = (x / y_m) * (x / 2.0d0)
    else if (x <= 7.2d+47) then
        tmp = (z / y_m) * (z / (-2.0d0))
    else
        tmp = (x * 0.5d0) / (y_m / x)
    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 t_0 = ((y_m - z) * (y_m + z)) / (y_m * 2.0);
	double tmp;
	if (x <= 4.7e-242) {
		tmp = t_0;
	} else if (x <= 1.1e-229) {
		tmp = y_m * 0.5;
	} else if (x <= 4.6e-6) {
		tmp = t_0;
	} else if (x <= 370000.0) {
		tmp = (x / y_m) * (x / 2.0);
	} else if (x <= 7.2e+47) {
		tmp = (z / y_m) * (z / -2.0);
	} else {
		tmp = (x * 0.5) / (y_m / x);
	}
	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 = ((y_m - z) * (y_m + z)) / (y_m * 2.0)
	tmp = 0
	if x <= 4.7e-242:
		tmp = t_0
	elif x <= 1.1e-229:
		tmp = y_m * 0.5
	elif x <= 4.6e-6:
		tmp = t_0
	elif x <= 370000.0:
		tmp = (x / y_m) * (x / 2.0)
	elif x <= 7.2e+47:
		tmp = (z / y_m) * (z / -2.0)
	else:
		tmp = (x * 0.5) / (y_m / x)
	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 = Float64(Float64(Float64(y_m - z) * Float64(y_m + z)) / Float64(y_m * 2.0))
	tmp = 0.0
	if (x <= 4.7e-242)
		tmp = t_0;
	elseif (x <= 1.1e-229)
		tmp = Float64(y_m * 0.5);
	elseif (x <= 4.6e-6)
		tmp = t_0;
	elseif (x <= 370000.0)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	elseif (x <= 7.2e+47)
		tmp = Float64(Float64(z / y_m) * Float64(z / -2.0));
	else
		tmp = Float64(Float64(x * 0.5) / Float64(y_m / x));
	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 = ((y_m - z) * (y_m + z)) / (y_m * 2.0);
	tmp = 0.0;
	if (x <= 4.7e-242)
		tmp = t_0;
	elseif (x <= 1.1e-229)
		tmp = y_m * 0.5;
	elseif (x <= 4.6e-6)
		tmp = t_0;
	elseif (x <= 370000.0)
		tmp = (x / y_m) * (x / 2.0);
	elseif (x <= 7.2e+47)
		tmp = (z / y_m) * (z / -2.0);
	else
		tmp = (x * 0.5) / (y_m / x);
	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[(N[(N[(y$95$m - z), $MachinePrecision] * N[(y$95$m + z), $MachinePrecision]), $MachinePrecision] / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * If[LessEqual[x, 4.7e-242], t$95$0, If[LessEqual[x, 1.1e-229], N[(y$95$m * 0.5), $MachinePrecision], If[LessEqual[x, 4.6e-6], t$95$0, If[LessEqual[x, 370000.0], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+47], N[(N[(z / y$95$m), $MachinePrecision] * N[(z / -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] / N[(y$95$m / x), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 5: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 6.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{\left(x \cdot x + y_m \cdot y_m\right) - z \cdot z}{y_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y_m \cdot 0.5\\ \end{array} \end{array} \]

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 6.1e+152)
    (/ (- (+ (* 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 <= 6.1e+152) {
		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 <= 6.1d+152) 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 <= 6.1e+152) {
		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 <= 6.1e+152:
		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 <= 6.1e+152)
		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 <= 6.1e+152)
		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, 6.1e+152], 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 6: 53.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y_m}\right)\\ \mathbf{else}:\\ \;\;\;\;y_m \cdot 0.5\\ \end{array} \end{array} \]

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 1.95e+71) (* x (* x (/ 0.5 y_m))) (* 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 <= 1.95e+71) {
		tmp = x * (x * (0.5 / y_m));
	} 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 <= 1.95d+71) then
        tmp = x * (x * (0.5d0 / y_m))
    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 <= 1.95e+71) {
		tmp = x * (x * (0.5 / y_m));
	} 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 <= 1.95e+71:
		tmp = x * (x * (0.5 / y_m))
	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 <= 1.95e+71)
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	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 <= 1.95e+71)
		tmp = x * (x * (0.5 / y_m));
	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, 1.95e+71], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y$95$m * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 53.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y_m} \cdot \frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;y_m \cdot 0.5\\ \end{array} \end{array} \]

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 2.1e+69) (* (/ x y_m) (/ x 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 <= 2.1e+69) {
		tmp = (x / y_m) * (x / 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 <= 2.1d+69) then
        tmp = (x / y_m) * (x / 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 <= 2.1e+69) {
		tmp = (x / y_m) * (x / 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 <= 2.1e+69:
		tmp = (x / y_m) * (x / 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 <= 2.1e+69)
		tmp = Float64(Float64(x / y_m) * Float64(x / 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 <= 2.1e+69)
		tmp = (x / y_m) * (x / 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, 2.1e+69], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], N[(y$95$m * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 33.7% 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 2023343 
(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)))