Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B

Percentage Accurate: 99.9% → 99.9%

Time: 4.7s

Alternatives: 7

Speedup: 1.0×

• 26.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot 2}\\ t_2 := -0.5 \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-200}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t 2.0))) (t_2 (* -0.5 (/ z t))))
   (if (<= x -1.35e+140)
     t_1
     (if (<= x -1.2e+114)
       t_2
       (if (<= x -6.2e+75) t_1 (if (<= x 3.5e-200) t_2 (/ y (* t 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * 2.0);
	double t_2 = -0.5 * (z / t);
	double tmp;
	if (x <= -1.35e+140) {
		tmp = t_1;
	} else if (x <= -1.2e+114) {
		tmp = t_2;
	} else if (x <= -6.2e+75) {
		tmp = t_1;
	} else if (x <= 3.5e-200) {
		tmp = t_2;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t * 2.0d0)
    t_2 = (-0.5d0) * (z / t)
    if (x <= (-1.35d+140)) then
        tmp = t_1
    else if (x <= (-1.2d+114)) then
        tmp = t_2
    else if (x <= (-6.2d+75)) then
        tmp = t_1
    else if (x <= 3.5d-200) then
        tmp = t_2
    else
        tmp = y / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * 2.0);
	double t_2 = -0.5 * (z / t);
	double tmp;
	if (x <= -1.35e+140) {
		tmp = t_1;
	} else if (x <= -1.2e+114) {
		tmp = t_2;
	} else if (x <= -6.2e+75) {
		tmp = t_1;
	} else if (x <= 3.5e-200) {
		tmp = t_2;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * 2.0)
	t_2 = -0.5 * (z / t)
	tmp = 0
	if x <= -1.35e+140:
		tmp = t_1
	elif x <= -1.2e+114:
		tmp = t_2
	elif x <= -6.2e+75:
		tmp = t_1
	elif x <= 3.5e-200:
		tmp = t_2
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * 2.0))
	t_2 = Float64(-0.5 * Float64(z / t))
	tmp = 0.0
	if (x <= -1.35e+140)
		tmp = t_1;
	elseif (x <= -1.2e+114)
		tmp = t_2;
	elseif (x <= -6.2e+75)
		tmp = t_1;
	elseif (x <= 3.5e-200)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * 2.0);
	t_2 = -0.5 * (z / t);
	tmp = 0.0;
	if (x <= -1.35e+140)
		tmp = t_1;
	elseif (x <= -1.2e+114)
		tmp = t_2;
	elseif (x <= -6.2e+75)
		tmp = t_1;
	elseif (x <= 3.5e-200)
		tmp = t_2;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+140], t$95$1, If[LessEqual[x, -1.2e+114], t$95$2, If[LessEqual[x, -6.2e+75], t$95$1, If[LessEqual[x, 3.5e-200], t$95$2, N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35000000000000009e140 or -1.2e114 < x < -6.2000000000000002e75

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.1%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]

   if -1.35000000000000009e140 < x < -1.2e114 or -6.2000000000000002e75 < x < 3.50000000000000023e-200

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.6%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   4. Taylor expanded in x around 0 53.5%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]

   if 3.50000000000000023e-200 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 27.7%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40} \lor \neg \left(z \leq 1.6 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e+40) (not (<= z 1.6e-15)))
   (/ (- x z) (* t 2.0))
   (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+40) || !(z <= 1.6e-15)) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2d+40)) .or. (.not. (z <= 1.6d-15))) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (x + y) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+40) || !(z <= 1.6e-15)) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e+40) or not (z <= 1.6e-15):
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e+40) || !(z <= 1.6e-15))
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e+40) || ~((z <= 1.6e-15)))
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e+40], N[Not[LessEqual[z, 1.6e-15]], $MachinePrecision]], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000006e40 or 1.6e-15 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.5%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -2.00000000000000006e40 < z < 1.6e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.2%

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

      1. +-commutative 95.2%

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

   5. Simplified 95.2%

      \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40} \lor \neg \left(z \leq 1.6 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+142} \lor \neg \left(z \leq 7.8 \cdot 10^{+108}\right):\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e+142) (not (<= z 7.8e+108)))
   (* -0.5 (/ z t))
   (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e+142) || !(z <= 7.8e+108)) {
		tmp = -0.5 * (z / t);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.6d+142)) .or. (.not. (z <= 7.8d+108))) then
        tmp = (-0.5d0) * (z / t)
    else
        tmp = (x + y) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e+142) || !(z <= 7.8e+108)) {
		tmp = -0.5 * (z / t);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.6e+142) or not (z <= 7.8e+108):
		tmp = -0.5 * (z / t)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.6e+142) || !(z <= 7.8e+108))
		tmp = Float64(-0.5 * Float64(z / t));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.6e+142) || ~((z <= 7.8e+108)))
		tmp = -0.5 * (z / t);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e+142], N[Not[LessEqual[z, 7.8e+108]], $MachinePrecision]], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000004e142 or 7.79999999999999969e108 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.1%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   4. Taylor expanded in x around 0 83.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]

   if -6.6000000000000004e142 < z < 7.79999999999999969e108

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 88.0%

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

      1. +-commutative 88.0%

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

   5. Simplified 88.0%

      \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+142} \lor \neg \left(z \leq 7.8 \cdot 10^{+108}\right):\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+114} \lor \neg \left(z \leq 6.3 \cdot 10^{+72}\right):\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.6e+114) (not (<= z 6.3e+72)))
   (* -0.5 (/ z t))
   (/ x (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e+114) || !(z <= 6.3e+72)) {
		tmp = -0.5 * (z / t);
	} else {
		tmp = x / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.6d+114)) .or. (.not. (z <= 6.3d+72))) then
        tmp = (-0.5d0) * (z / t)
    else
        tmp = x / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e+114) || !(z <= 6.3e+72)) {
		tmp = -0.5 * (z / t);
	} else {
		tmp = x / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.6e+114) or not (z <= 6.3e+72):
		tmp = -0.5 * (z / t)
	else:
		tmp = x / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.6e+114) || !(z <= 6.3e+72))
		tmp = Float64(-0.5 * Float64(z / t));
	else
		tmp = Float64(x / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.6e+114) || ~((z <= 6.3e+72)))
		tmp = -0.5 * (z / t);
	else
		tmp = x / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.6e+114], N[Not[LessEqual[z, 6.3e+72]], $MachinePrecision]], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000001e114 or 6.29999999999999963e72 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.0%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   4. Taylor expanded in x around 0 78.2%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]

   if -4.6000000000000001e114 < z < 6.29999999999999963e72

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 52.8%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+114} \lor \neg \left(z \leq 6.3 \cdot 10^{+72}\right):\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-77}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6e-77) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e-77) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 6d-77) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e-77) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6e-77:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6e-77)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6e-77)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6e-77], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.00000000000000033e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.3%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if 6.00000000000000033e-77 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 69.5%

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 36.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot \frac{z}{t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 72.5%

   \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

4. Taylor expanded in x around 0 36.8%

   \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))