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

Percentage Accurate: 69.1% → 99.9%

Time: 10.7s

Alternatives: 10

Speedup: 1.2×

• 41.3% 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: 69.1% 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: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((x + z) * ((x - z) / y)) + 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 + z) * ((x - z) / y)) + y) / 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.3%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 43.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot -0.5}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x \cdot x}{y}}{2}\\ \mathbf{elif}\;y \leq 0.0145:\\ \;\;\;\;z \cdot \left(\frac{z}{y} \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4e-169)
   (/ (* z -0.5) (/ y z))
   (if (<= y 3.3e-69)
     (/ (/ (* x x) y) 2.0)
     (if (<= y 0.0145) (* z (* (/ z y) -0.5)) (/ y 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4e-169) {
		tmp = (z * -0.5) / (y / z);
	} else if (y <= 3.3e-69) {
		tmp = ((x * x) / y) / 2.0;
	} else if (y <= 0.0145) {
		tmp = z * ((z / y) * -0.5);
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 4d-169) then
        tmp = (z * (-0.5d0)) / (y / z)
    else if (y <= 3.3d-69) then
        tmp = ((x * x) / y) / 2.0d0
    else if (y <= 0.0145d0) then
        tmp = z * ((z / y) * (-0.5d0))
    else
        tmp = y / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4e-169) {
		tmp = (z * -0.5) / (y / z);
	} else if (y <= 3.3e-69) {
		tmp = ((x * x) / y) / 2.0;
	} else if (y <= 0.0145) {
		tmp = z * ((z / y) * -0.5);
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4e-169:
		tmp = (z * -0.5) / (y / z)
	elif y <= 3.3e-69:
		tmp = ((x * x) / y) / 2.0
	elif y <= 0.0145:
		tmp = z * ((z / y) * -0.5)
	else:
		tmp = y / 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4e-169)
		tmp = Float64(Float64(z * -0.5) / Float64(y / z));
	elseif (y <= 3.3e-69)
		tmp = Float64(Float64(Float64(x * x) / y) / 2.0);
	elseif (y <= 0.0145)
		tmp = Float64(z * Float64(Float64(z / y) * -0.5));
	else
		tmp = Float64(y / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4e-169)
		tmp = (z * -0.5) / (y / z);
	elseif (y <= 3.3e-69)
		tmp = ((x * x) / y) / 2.0;
	elseif (y <= 0.0145)
		tmp = z * ((z / y) * -0.5);
	else
		tmp = y / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4e-169], N[(N[(z * -0.5), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-69], N[(N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[y, 0.0145], N[(z * N[(N[(z / y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(y / 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 4.00000000000000008e-169

   1. Initial program 80.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.00000000000000008e-169 < y < 3.3e-69

   1. Initial program 96.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 3.3e-69 < y < 0.0145000000000000007

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.0145000000000000007 < y

   1. Initial program 37.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 43.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot -0.5}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{elif}\;y \leq 0.038:\\ \;\;\;\;z \cdot \left(\frac{z}{y} \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.05e-169)
   (/ (* z -0.5) (/ y z))
   (if (<= y 3.3e-69)
     (* x (* x (/ 0.5 y)))
     (if (<= y 0.038) (* z (* (/ z y) -0.5)) (/ y 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.05e-169) {
		tmp = (z * -0.5) / (y / z);
	} else if (y <= 3.3e-69) {
		tmp = x * (x * (0.5 / y));
	} else if (y <= 0.038) {
		tmp = z * ((z / y) * -0.5);
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.05d-169) then
        tmp = (z * (-0.5d0)) / (y / z)
    else if (y <= 3.3d-69) then
        tmp = x * (x * (0.5d0 / y))
    else if (y <= 0.038d0) then
        tmp = z * ((z / y) * (-0.5d0))
    else
        tmp = y / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.05e-169) {
		tmp = (z * -0.5) / (y / z);
	} else if (y <= 3.3e-69) {
		tmp = x * (x * (0.5 / y));
	} else if (y <= 0.038) {
		tmp = z * ((z / y) * -0.5);
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.05e-169:
		tmp = (z * -0.5) / (y / z)
	elif y <= 3.3e-69:
		tmp = x * (x * (0.5 / y))
	elif y <= 0.038:
		tmp = z * ((z / y) * -0.5)
	else:
		tmp = y / 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.05e-169)
		tmp = Float64(Float64(z * -0.5) / Float64(y / z));
	elseif (y <= 3.3e-69)
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	elseif (y <= 0.038)
		tmp = Float64(z * Float64(Float64(z / y) * -0.5));
	else
		tmp = Float64(y / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.05e-169)
		tmp = (z * -0.5) / (y / z);
	elseif (y <= 3.3e-69)
		tmp = x * (x * (0.5 / y));
	elseif (y <= 0.038)
		tmp = z * ((z / y) * -0.5);
	else
		tmp = y / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.05e-169], N[(N[(z * -0.5), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-69], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.038], N[(z * N[(N[(z / y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(y / 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 1.05e-169

   1. Initial program 80.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.05e-169 < y < 3.3e-69

   1. Initial program 96.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 3.3e-69 < y < 0.0379999999999999991

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.0379999999999999991 < y

   1. Initial program 37.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 43.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\frac{z}{y} \cdot -0.5\right)\\ \mathbf{if}\;y \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{elif}\;y \leq 0.42:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (/ z y) -0.5))))
   (if (<= y 4e-170)
     t_0
     (if (<= y 3e-69) (* x (* x (/ 0.5 y))) (if (<= y 0.42) t_0 (/ y 2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((z / y) * -0.5);
	double tmp;
	if (y <= 4e-170) {
		tmp = t_0;
	} else if (y <= 3e-69) {
		tmp = x * (x * (0.5 / y));
	} else if (y <= 0.42) {
		tmp = t_0;
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((z / y) * (-0.5d0))
    if (y <= 4d-170) then
        tmp = t_0
    else if (y <= 3d-69) then
        tmp = x * (x * (0.5d0 / y))
    else if (y <= 0.42d0) then
        tmp = t_0
    else
        tmp = y / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((z / y) * -0.5);
	double tmp;
	if (y <= 4e-170) {
		tmp = t_0;
	} else if (y <= 3e-69) {
		tmp = x * (x * (0.5 / y));
	} else if (y <= 0.42) {
		tmp = t_0;
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((z / y) * -0.5)
	tmp = 0
	if y <= 4e-170:
		tmp = t_0
	elif y <= 3e-69:
		tmp = x * (x * (0.5 / y))
	elif y <= 0.42:
		tmp = t_0
	else:
		tmp = y / 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(z / y) * -0.5))
	tmp = 0.0
	if (y <= 4e-170)
		tmp = t_0;
	elseif (y <= 3e-69)
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	elseif (y <= 0.42)
		tmp = t_0;
	else
		tmp = Float64(y / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((z / y) * -0.5);
	tmp = 0.0;
	if (y <= 4e-170)
		tmp = t_0;
	elseif (y <= 3e-69)
		tmp = x * (x * (0.5 / y));
	elseif (y <= 0.42)
		tmp = t_0;
	else
		tmp = y / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(z / y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 4e-170], t$95$0, If[LessEqual[y, 3e-69], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.42], t$95$0, N[(y / 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.99999999999999993e-170 or 2.99999999999999989e-69 < y < 0.419999999999999984

   1. Initial program 81.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 3.99999999999999993e-170 < y < 2.99999999999999989e-69

   1. Initial program 96.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 0.419999999999999984 < y

   1. Initial program 37.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 91.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{+303}:\\ \;\;\;\;\frac{y + \frac{x \cdot x - z \cdot z}{y}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}} + y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x x) 1e+303)
   (/ (+ y (/ (- (* x x) (* z z)) y)) 2.0)
   (/ (+ (/ x (/ y x)) y) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e+303) {
		tmp = (y + (((x * x) - (z * z)) / y)) / 2.0;
	} else {
		tmp = ((x / (y / x)) + y) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x * x) <= 1d+303) then
        tmp = (y + (((x * x) - (z * z)) / y)) / 2.0d0
    else
        tmp = ((x / (y / x)) + y) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e+303) {
		tmp = (y + (((x * x) - (z * z)) / y)) / 2.0;
	} else {
		tmp = ((x / (y / x)) + y) / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x * x) <= 1e+303:
		tmp = (y + (((x * x) - (z * z)) / y)) / 2.0
	else:
		tmp = ((x / (y / x)) + y) / 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * x) <= 1e+303)
		tmp = Float64(Float64(y + Float64(Float64(Float64(x * x) - Float64(z * z)) / y)) / 2.0);
	else
		tmp = Float64(Float64(Float64(x / Float64(y / x)) + y) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * x) <= 1e+303)
		tmp = (y + (((x * x) - (z * z)) / y)) / 2.0;
	else
		tmp = ((x / (y / x)) + y) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * x), $MachinePrecision], 1e+303], N[(N[(y + N[(N[(N[(x * x), $MachinePrecision] - N[(z * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1e303

   1. Initial program 78.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   if 1e303 < (*.f64 x x)

   1. Initial program 55.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 82.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{-162}:\\ \;\;\;\;\frac{y - \frac{z}{\frac{y}{z}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}} + y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x x) 1e-162)
   (/ (- y (/ z (/ y z))) 2.0)
   (/ (+ (/ x (/ y x)) y) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e-162) {
		tmp = (y - (z / (y / z))) / 2.0;
	} else {
		tmp = ((x / (y / x)) + y) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x * x) <= 1d-162) then
        tmp = (y - (z / (y / z))) / 2.0d0
    else
        tmp = ((x / (y / x)) + y) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e-162) {
		tmp = (y - (z / (y / z))) / 2.0;
	} else {
		tmp = ((x / (y / x)) + y) / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x * x) <= 1e-162:
		tmp = (y - (z / (y / z))) / 2.0
	else:
		tmp = ((x / (y / x)) + y) / 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * x) <= 1e-162)
		tmp = Float64(Float64(y - Float64(z / Float64(y / z))) / 2.0);
	else
		tmp = Float64(Float64(Float64(x / Float64(y / x)) + y) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * x) <= 1e-162)
		tmp = (y - (z / (y / z))) / 2.0;
	else
		tmp = ((x / (y / x)) + y) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * x), $MachinePrecision], 1e-162], N[(N[(y - N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 9.99999999999999954e-163

   1. Initial program 82.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 9.99999999999999954e-163 < (*.f64 x x)

   1. Initial program 66.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 79.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}} + y}{2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{z}{y} \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 2e+290) (/ (+ (/ x (/ y x)) y) 2.0) (* z (* (/ z y) -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 2e+290) {
		tmp = ((x / (y / x)) + y) / 2.0;
	} else {
		tmp = z * ((z / y) * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z * z) <= 2d+290) then
        tmp = ((x / (y / x)) + y) / 2.0d0
    else
        tmp = z * ((z / y) * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 2e+290) {
		tmp = ((x / (y / x)) + y) / 2.0;
	} else {
		tmp = z * ((z / y) * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 2e+290:
		tmp = ((x / (y / x)) + y) / 2.0
	else:
		tmp = z * ((z / y) * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 2e+290)
		tmp = Float64(Float64(Float64(x / Float64(y / x)) + y) / 2.0);
	else
		tmp = Float64(z * Float64(Float64(z / y) * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 2e+290)
		tmp = ((x / (y / x)) + y) / 2.0;
	else
		tmp = z * ((z / y) * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+290], N[(N[(N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] / 2.0), $MachinePrecision], N[(z * N[(N[(z / y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.00000000000000012e290

   1. Initial program 77.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if 2.00000000000000012e290 < (*.f64 z z)

   1. Initial program 55.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{y + \frac{x \cdot x}{y}}{2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{z}{y} \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 2e+290) (/ (+ y (/ (* x x) y)) 2.0) (* z (* (/ z y) -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 2e+290) {
		tmp = (y + ((x * x) / y)) / 2.0;
	} else {
		tmp = z * ((z / y) * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z * z) <= 2d+290) then
        tmp = (y + ((x * x) / y)) / 2.0d0
    else
        tmp = z * ((z / y) * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 2e+290) {
		tmp = (y + ((x * x) / y)) / 2.0;
	} else {
		tmp = z * ((z / y) * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 2e+290:
		tmp = (y + ((x * x) / y)) / 2.0
	else:
		tmp = z * ((z / y) * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 2e+290)
		tmp = Float64(Float64(y + Float64(Float64(x * x) / y)) / 2.0);
	else
		tmp = Float64(z * Float64(Float64(z / y) * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 2e+290)
		tmp = (y + ((x * x) / y)) / 2.0;
	else
		tmp = z * ((z / y) * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+290], N[(N[(y + N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(z * N[(N[(z / y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.00000000000000012e290

   1. Initial program 77.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 2.00000000000000012e290 < (*.f64 z z)

   1. Initial program 55.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 43.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.2e+43) (* x (* x (/ 0.5 y))) (/ y 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e+43) {
		tmp = x * (x * (0.5 / y));
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.2d+43) then
        tmp = x * (x * (0.5d0 / y))
    else
        tmp = y / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e+43) {
		tmp = x * (x * (0.5 / y));
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.2e+43:
		tmp = x * (x * (0.5 / y))
	else:
		tmp = y / 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.2e+43)
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	else
		tmp = Float64(y / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.2e+43)
		tmp = x * (x * (0.5 / y));
	else
		tmp = y / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.2e+43], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.20000000000000001e43

   1. Initial program 84.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 2.20000000000000001e43 < y

   1. Initial program 31.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 35.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{y}{2} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ y 2.0))

C

double code(double x, double y, double z) {
	return 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 = y / 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y / 2.0), $MachinePrecision]

Derivation

1. Initial program 72.3%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer Target 1: 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 2024111 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* y 1/2) (* (* (/ 1/2 y) (+ z x)) (- z x))))

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