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

Percentage Accurate: 93.3% → 97.2%

Time: 10.3s

Alternatives: 12

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{z - t}{\frac{a}{y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 85.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+163} \lor \neg \left(t_1 \leq 5 \cdot 10^{+62} \lor \neg \left(t_1 \leq 10^{+131}\right) \land t_1 \leq 5 \cdot 10^{+171}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)))
   (if (or (<= t_1 -4e+163)
           (not
            (or (<= t_1 5e+62) (and (not (<= t_1 1e+131)) (<= t_1 5e+171)))))
     (* (- z t) (/ y a))
     (- x (/ (* t y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if ((t_1 <= -4e+163) || !((t_1 <= 5e+62) || (!(t_1 <= 1e+131) && (t_1 <= 5e+171)))) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - ((t * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - t) * y) / a
    if ((t_1 <= (-4d+163)) .or. (.not. (t_1 <= 5d+62) .or. (.not. (t_1 <= 1d+131)) .and. (t_1 <= 5d+171))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x - ((t * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if ((t_1 <= -4e+163) || !((t_1 <= 5e+62) || (!(t_1 <= 1e+131) && (t_1 <= 5e+171)))) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / a
	tmp = 0
	if (t_1 <= -4e+163) or not ((t_1 <= 5e+62) or (not (t_1 <= 1e+131) and (t_1 <= 5e+171))):
		tmp = (z - t) * (y / a)
	else:
		tmp = x - ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	tmp = 0.0
	if ((t_1 <= -4e+163) || !((t_1 <= 5e+62) || (!(t_1 <= 1e+131) && (t_1 <= 5e+171))))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x - Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / a;
	tmp = 0.0;
	if ((t_1 <= -4e+163) || ~(((t_1 <= 5e+62) || (~((t_1 <= 1e+131)) && (t_1 <= 5e+171)))))
		tmp = (z - t) * (y / a);
	else
		tmp = x - ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+163], N[Not[Or[LessEqual[t$95$1, 5e+62], And[N[Not[LessEqual[t$95$1, 1e+131]], $MachinePrecision], LessEqual[t$95$1, 5e+171]]]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+163}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+62}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)))
   (if (<= t_1 -4e+163)
     (* (- z t) (/ y a))
     (if (<= t_1 5e+62) (- x (/ (* t y) a)) (/ (- z t) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if (t_1 <= -4e+163) {
		tmp = (z - t) * (y / a);
	} else if (t_1 <= 5e+62) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = (z - t) / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - t) * y) / a
    if (t_1 <= (-4d+163)) then
        tmp = (z - t) * (y / a)
    else if (t_1 <= 5d+62) then
        tmp = x - ((t * y) / a)
    else
        tmp = (z - t) / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if (t_1 <= -4e+163) {
		tmp = (z - t) * (y / a);
	} else if (t_1 <= 5e+62) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = (z - t) / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / a
	tmp = 0
	if t_1 <= -4e+163:
		tmp = (z - t) * (y / a)
	elif t_1 <= 5e+62:
		tmp = x - ((t * y) / a)
	else:
		tmp = (z - t) / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	tmp = 0.0
	if (t_1 <= -4e+163)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t_1 <= 5e+62)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	else
		tmp = Float64(Float64(z - t) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / a;
	tmp = 0.0;
	if (t_1 <= -4e+163)
		tmp = (z - t) * (y / a);
	elseif (t_1 <= 5e+62)
		tmp = x - ((t * y) / a);
	else
		tmp = (z - t) / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+163], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+62], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 49.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{a}\\ t_2 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z y) a)) (t_2 (* t (/ (- y) a))))
   (if (<= t -8.5e+177)
     t_2
     (if (<= t -1.05e-18)
       x
       (if (<= t -5.2e-90)
         t_1
         (if (<= t 1.25e-36)
           x
           (if (<= t 2.25e+17) t_1 (if (<= t 9.4e+139) x t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * y) / a;
	double t_2 = t * (-y / a);
	double tmp;
	if (t <= -8.5e+177) {
		tmp = t_2;
	} else if (t <= -1.05e-18) {
		tmp = x;
	} else if (t <= -5.2e-90) {
		tmp = t_1;
	} else if (t <= 1.25e-36) {
		tmp = x;
	} else if (t <= 2.25e+17) {
		tmp = t_1;
	} else if (t <= 9.4e+139) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * y) / a
    t_2 = t * (-y / a)
    if (t <= (-8.5d+177)) then
        tmp = t_2
    else if (t <= (-1.05d-18)) then
        tmp = x
    else if (t <= (-5.2d-90)) then
        tmp = t_1
    else if (t <= 1.25d-36) then
        tmp = x
    else if (t <= 2.25d+17) then
        tmp = t_1
    else if (t <= 9.4d+139) then
        tmp = x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * y) / a;
	double t_2 = t * (-y / a);
	double tmp;
	if (t <= -8.5e+177) {
		tmp = t_2;
	} else if (t <= -1.05e-18) {
		tmp = x;
	} else if (t <= -5.2e-90) {
		tmp = t_1;
	} else if (t <= 1.25e-36) {
		tmp = x;
	} else if (t <= 2.25e+17) {
		tmp = t_1;
	} else if (t <= 9.4e+139) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * y) / a
	t_2 = t * (-y / a)
	tmp = 0
	if t <= -8.5e+177:
		tmp = t_2
	elif t <= -1.05e-18:
		tmp = x
	elif t <= -5.2e-90:
		tmp = t_1
	elif t <= 1.25e-36:
		tmp = x
	elif t <= 2.25e+17:
		tmp = t_1
	elif t <= 9.4e+139:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * y) / a)
	t_2 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -8.5e+177)
		tmp = t_2;
	elseif (t <= -1.05e-18)
		tmp = x;
	elseif (t <= -5.2e-90)
		tmp = t_1;
	elseif (t <= 1.25e-36)
		tmp = x;
	elseif (t <= 2.25e+17)
		tmp = t_1;
	elseif (t <= 9.4e+139)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * y) / a;
	t_2 = t * (-y / a);
	tmp = 0.0;
	if (t <= -8.5e+177)
		tmp = t_2;
	elseif (t <= -1.05e-18)
		tmp = x;
	elseif (t <= -5.2e-90)
		tmp = t_1;
	elseif (t <= 1.25e-36)
		tmp = x;
	elseif (t <= 2.25e+17)
		tmp = t_1;
	elseif (t <= 9.4e+139)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+177], t$95$2, If[LessEqual[t, -1.05e-18], x, If[LessEqual[t, -5.2e-90], t$95$1, If[LessEqual[t, 1.25e-36], x, If[LessEqual[t, 2.25e+17], t$95$1, If[LessEqual[t, 9.4e+139], x, t$95$2]]]]]]]]

Derivation

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

Alternative 5: 48.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{a}\\ \mathbf{if}\;t \leq -2.02 \cdot 10^{+177}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z y) a)))
   (if (<= t -2.02e+177)
     (/ (- y) (/ a t))
     (if (<= t -9.2e-20)
       x
       (if (<= t -7.5e-83)
         t_1
         (if (<= t 1.2e-36)
           x
           (if (<= t 7.1e+15)
             t_1
             (if (<= t 2.4e+140) x (* t (/ (- y) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * y) / a;
	double tmp;
	if (t <= -2.02e+177) {
		tmp = -y / (a / t);
	} else if (t <= -9.2e-20) {
		tmp = x;
	} else if (t <= -7.5e-83) {
		tmp = t_1;
	} else if (t <= 1.2e-36) {
		tmp = x;
	} else if (t <= 7.1e+15) {
		tmp = t_1;
	} else if (t <= 2.4e+140) {
		tmp = x;
	} else {
		tmp = t * (-y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) / a
    if (t <= (-2.02d+177)) then
        tmp = -y / (a / t)
    else if (t <= (-9.2d-20)) then
        tmp = x
    else if (t <= (-7.5d-83)) then
        tmp = t_1
    else if (t <= 1.2d-36) then
        tmp = x
    else if (t <= 7.1d+15) then
        tmp = t_1
    else if (t <= 2.4d+140) then
        tmp = x
    else
        tmp = t * (-y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * y) / a;
	double tmp;
	if (t <= -2.02e+177) {
		tmp = -y / (a / t);
	} else if (t <= -9.2e-20) {
		tmp = x;
	} else if (t <= -7.5e-83) {
		tmp = t_1;
	} else if (t <= 1.2e-36) {
		tmp = x;
	} else if (t <= 7.1e+15) {
		tmp = t_1;
	} else if (t <= 2.4e+140) {
		tmp = x;
	} else {
		tmp = t * (-y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * y) / a
	tmp = 0
	if t <= -2.02e+177:
		tmp = -y / (a / t)
	elif t <= -9.2e-20:
		tmp = x
	elif t <= -7.5e-83:
		tmp = t_1
	elif t <= 1.2e-36:
		tmp = x
	elif t <= 7.1e+15:
		tmp = t_1
	elif t <= 2.4e+140:
		tmp = x
	else:
		tmp = t * (-y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * y) / a)
	tmp = 0.0
	if (t <= -2.02e+177)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= -9.2e-20)
		tmp = x;
	elseif (t <= -7.5e-83)
		tmp = t_1;
	elseif (t <= 1.2e-36)
		tmp = x;
	elseif (t <= 7.1e+15)
		tmp = t_1;
	elseif (t <= 2.4e+140)
		tmp = x;
	else
		tmp = Float64(t * Float64(Float64(-y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * y) / a;
	tmp = 0.0;
	if (t <= -2.02e+177)
		tmp = -y / (a / t);
	elseif (t <= -9.2e-20)
		tmp = x;
	elseif (t <= -7.5e-83)
		tmp = t_1;
	elseif (t <= 1.2e-36)
		tmp = x;
	elseif (t <= 7.1e+15)
		tmp = t_1;
	elseif (t <= 2.4e+140)
		tmp = x;
	else
		tmp = t * (-y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -2.02e+177], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-20], x, If[LessEqual[t, -7.5e-83], t$95$1, If[LessEqual[t, 1.2e-36], x, If[LessEqual[t, 7.1e+15], t$95$1, If[LessEqual[t, 2.4e+140], x, N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 6: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.48 \cdot 10^{+181} \lor \neg \left(t \leq 8.2 \cdot 10^{+139}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.48e+181) (not (<= t 8.2e+139)))
   (* (- z t) (/ y a))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.48e+181) || !(t <= 8.2e+139)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.48d+181)) .or. (.not. (t <= 8.2d+139))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.48e+181) || !(t <= 8.2e+139)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.48e+181) or not (t <= 8.2e+139):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.48e+181) || !(t <= 8.2e+139))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.48e+181) || ~((t <= 8.2e+139)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.48e+181], N[Not[LessEqual[t, 8.2e+139]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+135}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-36) x (if (<= a 2.75e+135) (* (- z t) (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-36) {
		tmp = x;
	} else if (a <= 2.75e+135) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.8d-36)) then
        tmp = x
    else if (a <= 2.75d+135) then
        tmp = (z - t) * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-36) {
		tmp = x;
	} else if (a <= 2.75e+135) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-36:
		tmp = x
	elif a <= 2.75e+135:
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-36)
		tmp = x;
	elseif (a <= 2.75e+135)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e-36)
		tmp = x;
	elseif (a <= 2.75e+135)
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-36], x, If[LessEqual[a, 2.75e+135], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

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

Alternative 8: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+15)
   (- x (* t (/ y a)))
   (if (<= t 6.8e+137) (+ x (* y (/ z a))) (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+15) {
		tmp = x - (t * (y / a));
	} else if (t <= 6.8e+137) {
		tmp = x + (y * (z / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.3d+15)) then
        tmp = x - (t * (y / a))
    else if (t <= 6.8d+137) then
        tmp = x + (y * (z / a))
    else
        tmp = (z - t) * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+15) {
		tmp = x - (t * (y / a));
	} else if (t <= 6.8e+137) {
		tmp = x + (y * (z / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e+15:
		tmp = x - (t * (y / a))
	elif t <= 6.8e+137:
		tmp = x + (y * (z / a))
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+15)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 6.8e+137)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(z - t) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e+15)
		tmp = x - (t * (y / a));
	elseif (t <= 6.8e+137)
		tmp = x + (y * (z / a));
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+15], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+137], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-13} \lor \neg \left(y \leq 3.2 \cdot 10^{+191}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.7e-13) (not (<= y 3.2e+191))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e-13) || !(y <= 3.2e+191)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.7d-13)) .or. (.not. (y <= 3.2d+191))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e-13) || !(y <= 3.2e+191)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.7e-13) or not (y <= 3.2e+191):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.7e-13) || !(y <= 3.2e+191))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.7e-13) || ~((y <= 3.2e+191)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.7e-13], N[Not[LessEqual[y, 3.2e+191]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

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

Alternative 10: 47.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+194}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.8e-13) (* y (/ z a)) (if (<= y 1.85e+194) x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e-13) {
		tmp = y * (z / a);
	} else if (y <= 1.85e+194) {
		tmp = x;
	} else {
		tmp = (z * y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.8d-13)) then
        tmp = y * (z / a)
    else if (y <= 1.85d+194) then
        tmp = x
    else
        tmp = (z * y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e-13) {
		tmp = y * (z / a);
	} else if (y <= 1.85e+194) {
		tmp = x;
	} else {
		tmp = (z * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.8e-13:
		tmp = y * (z / a)
	elif y <= 1.85e+194:
		tmp = x
	else:
		tmp = (z * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.8e-13)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 1.85e+194)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.8e-13)
		tmp = y * (z / a);
	elseif (y <= 1.85e+194)
		tmp = x;
	else
		tmp = (z * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.8e-13], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+194], x, N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

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

Alternative 11: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 12: 39.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

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

Developer target: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))