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

Percentage Accurate: 93.7% → 99.3%

Time: 10.9s

Alternatives: 11

Speedup: 1.0×

• 24.3% 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: 93.7% 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: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-36} \lor \neg \left(a \leq 2.6 \cdot 10^{-52}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1e-36) (not (<= a 2.6e-52)))
   (+ x (/ y (/ a (- z t))))
   (+ x (/ (* (- z t) y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1e-36) || !(a <= 2.6e-52)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (((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 ((a <= (-1d-36)) .or. (.not. (a <= 2.6d-52))) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + (((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 ((a <= -1e-36) || !(a <= 2.6e-52)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (((z - t) * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1e-36) or not (a <= 2.6e-52):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + (((z - t) * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1e-36) || !(a <= 2.6e-52))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1e-36) || ~((a <= 2.6e-52)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + (((z - t) * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1e-36], N[Not[LessEqual[a, 2.6e-52]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := \frac{t \cdot y}{-a}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+201}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (/ (* t y) (- a))))
   (if (<= t -3.3e+203)
     t_2
     (if (<= t -2.7e+159)
       t_1
       (if (<= t -2e+54)
         t_2
         (if (<= t 1.15e+69)
           t_1
           (if (<= t 3.4e+92)
             t_2
             (if (<= t 2.15e+201) t_1 (* t (- (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = (t * y) / -a;
	double tmp;
	if (t <= -3.3e+203) {
		tmp = t_2;
	} else if (t <= -2.7e+159) {
		tmp = t_1;
	} else if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= 1.15e+69) {
		tmp = t_1;
	} else if (t <= 3.4e+92) {
		tmp = t_2;
	} else if (t <= 2.15e+201) {
		tmp = t_1;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    t_2 = (t * y) / -a
    if (t <= (-3.3d+203)) then
        tmp = t_2
    else if (t <= (-2.7d+159)) then
        tmp = t_1
    else if (t <= (-2d+54)) then
        tmp = t_2
    else if (t <= 1.15d+69) then
        tmp = t_1
    else if (t <= 3.4d+92) then
        tmp = t_2
    else if (t <= 2.15d+201) then
        tmp = t_1
    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 = x + (y / (a / z));
	double t_2 = (t * y) / -a;
	double tmp;
	if (t <= -3.3e+203) {
		tmp = t_2;
	} else if (t <= -2.7e+159) {
		tmp = t_1;
	} else if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= 1.15e+69) {
		tmp = t_1;
	} else if (t <= 3.4e+92) {
		tmp = t_2;
	} else if (t <= 2.15e+201) {
		tmp = t_1;
	} else {
		tmp = t * -(y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = (t * y) / -a
	tmp = 0
	if t <= -3.3e+203:
		tmp = t_2
	elif t <= -2.7e+159:
		tmp = t_1
	elif t <= -2e+54:
		tmp = t_2
	elif t <= 1.15e+69:
		tmp = t_1
	elif t <= 3.4e+92:
		tmp = t_2
	elif t <= 2.15e+201:
		tmp = t_1
	else:
		tmp = t * -(y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(Float64(t * y) / Float64(-a))
	tmp = 0.0
	if (t <= -3.3e+203)
		tmp = t_2;
	elseif (t <= -2.7e+159)
		tmp = t_1;
	elseif (t <= -2e+54)
		tmp = t_2;
	elseif (t <= 1.15e+69)
		tmp = t_1;
	elseif (t <= 3.4e+92)
		tmp = t_2;
	elseif (t <= 2.15e+201)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = (t * y) / -a;
	tmp = 0.0;
	if (t <= -3.3e+203)
		tmp = t_2;
	elseif (t <= -2.7e+159)
		tmp = t_1;
	elseif (t <= -2e+54)
		tmp = t_2;
	elseif (t <= 1.15e+69)
		tmp = t_1;
	elseif (t <= 3.4e+92)
		tmp = t_2;
	elseif (t <= 2.15e+201)
		tmp = t_1;
	else
		tmp = t * -(y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision]}, If[LessEqual[t, -3.3e+203], t$95$2, If[LessEqual[t, -2.7e+159], t$95$1, If[LessEqual[t, -2e+54], t$95$2, If[LessEqual[t, 1.15e+69], t$95$1, If[LessEqual[t, 3.4e+92], t$95$2, If[LessEqual[t, 2.15e+201], t$95$1, N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 3: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := \frac{t \cdot y}{-a}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (/ (* t y) (- a))))
   (if (<= t -2.7e+203)
     t_2
     (if (<= t -3.4e+159)
       t_1
       (if (<= t -2e+54)
         t_2
         (if (<= t 1.15e+69)
           (+ x (* y (/ z a)))
           (if (<= t 2.75e+91)
             t_2
             (if (<= t 1.3e+202) t_1 (* t (- (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = (t * y) / -a;
	double tmp;
	if (t <= -2.7e+203) {
		tmp = t_2;
	} else if (t <= -3.4e+159) {
		tmp = t_1;
	} else if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= 1.15e+69) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.75e+91) {
		tmp = t_2;
	} else if (t <= 1.3e+202) {
		tmp = t_1;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    t_2 = (t * y) / -a
    if (t <= (-2.7d+203)) then
        tmp = t_2
    else if (t <= (-3.4d+159)) then
        tmp = t_1
    else if (t <= (-2d+54)) then
        tmp = t_2
    else if (t <= 1.15d+69) then
        tmp = x + (y * (z / a))
    else if (t <= 2.75d+91) then
        tmp = t_2
    else if (t <= 1.3d+202) then
        tmp = t_1
    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 = x + (y / (a / z));
	double t_2 = (t * y) / -a;
	double tmp;
	if (t <= -2.7e+203) {
		tmp = t_2;
	} else if (t <= -3.4e+159) {
		tmp = t_1;
	} else if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= 1.15e+69) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.75e+91) {
		tmp = t_2;
	} else if (t <= 1.3e+202) {
		tmp = t_1;
	} else {
		tmp = t * -(y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = (t * y) / -a
	tmp = 0
	if t <= -2.7e+203:
		tmp = t_2
	elif t <= -3.4e+159:
		tmp = t_1
	elif t <= -2e+54:
		tmp = t_2
	elif t <= 1.15e+69:
		tmp = x + (y * (z / a))
	elif t <= 2.75e+91:
		tmp = t_2
	elif t <= 1.3e+202:
		tmp = t_1
	else:
		tmp = t * -(y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(Float64(t * y) / Float64(-a))
	tmp = 0.0
	if (t <= -2.7e+203)
		tmp = t_2;
	elseif (t <= -3.4e+159)
		tmp = t_1;
	elseif (t <= -2e+54)
		tmp = t_2;
	elseif (t <= 1.15e+69)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.75e+91)
		tmp = t_2;
	elseif (t <= 1.3e+202)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = (t * y) / -a;
	tmp = 0.0;
	if (t <= -2.7e+203)
		tmp = t_2;
	elseif (t <= -3.4e+159)
		tmp = t_1;
	elseif (t <= -2e+54)
		tmp = t_2;
	elseif (t <= 1.15e+69)
		tmp = x + (y * (z / a));
	elseif (t <= 2.75e+91)
		tmp = t_2;
	elseif (t <= 1.3e+202)
		tmp = t_1;
	else
		tmp = t * -(y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision]}, If[LessEqual[t, -2.7e+203], t$95$2, If[LessEqual[t, -3.4e+159], t$95$1, If[LessEqual[t, -2e+54], t$95$2, If[LessEqual[t, 1.15e+69], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.75e+91], t$95$2, If[LessEqual[t, 1.3e+202], t$95$1, N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := \frac{t \cdot y}{-a}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+201}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (/ (* t y) (- a))))
   (if (<= t -3.3e+203)
     t_2
     (if (<= t -8.2e+92)
       t_1
       (if (<= t -2e+54)
         t_2
         (if (<= t 1.1e+69)
           t_1
           (if (<= t 3.4e+92)
             t_2
             (if (<= t 2.1e+201) t_1 (* t (- (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = (t * y) / -a;
	double tmp;
	if (t <= -3.3e+203) {
		tmp = t_2;
	} else if (t <= -8.2e+92) {
		tmp = t_1;
	} else if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= 1.1e+69) {
		tmp = t_1;
	} else if (t <= 3.4e+92) {
		tmp = t_2;
	} else if (t <= 2.1e+201) {
		tmp = t_1;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = (t * y) / -a
    if (t <= (-3.3d+203)) then
        tmp = t_2
    else if (t <= (-8.2d+92)) then
        tmp = t_1
    else if (t <= (-2d+54)) then
        tmp = t_2
    else if (t <= 1.1d+69) then
        tmp = t_1
    else if (t <= 3.4d+92) then
        tmp = t_2
    else if (t <= 2.1d+201) then
        tmp = t_1
    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 = x + (z * (y / a));
	double t_2 = (t * y) / -a;
	double tmp;
	if (t <= -3.3e+203) {
		tmp = t_2;
	} else if (t <= -8.2e+92) {
		tmp = t_1;
	} else if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= 1.1e+69) {
		tmp = t_1;
	} else if (t <= 3.4e+92) {
		tmp = t_2;
	} else if (t <= 2.1e+201) {
		tmp = t_1;
	} else {
		tmp = t * -(y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = (t * y) / -a
	tmp = 0
	if t <= -3.3e+203:
		tmp = t_2
	elif t <= -8.2e+92:
		tmp = t_1
	elif t <= -2e+54:
		tmp = t_2
	elif t <= 1.1e+69:
		tmp = t_1
	elif t <= 3.4e+92:
		tmp = t_2
	elif t <= 2.1e+201:
		tmp = t_1
	else:
		tmp = t * -(y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(Float64(t * y) / Float64(-a))
	tmp = 0.0
	if (t <= -3.3e+203)
		tmp = t_2;
	elseif (t <= -8.2e+92)
		tmp = t_1;
	elseif (t <= -2e+54)
		tmp = t_2;
	elseif (t <= 1.1e+69)
		tmp = t_1;
	elseif (t <= 3.4e+92)
		tmp = t_2;
	elseif (t <= 2.1e+201)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = (t * y) / -a;
	tmp = 0.0;
	if (t <= -3.3e+203)
		tmp = t_2;
	elseif (t <= -8.2e+92)
		tmp = t_1;
	elseif (t <= -2e+54)
		tmp = t_2;
	elseif (t <= 1.1e+69)
		tmp = t_1;
	elseif (t <= 3.4e+92)
		tmp = t_2;
	elseif (t <= 2.1e+201)
		tmp = t_1;
	else
		tmp = t * -(y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision]}, If[LessEqual[t, -3.3e+203], t$95$2, If[LessEqual[t, -8.2e+92], t$95$1, If[LessEqual[t, -2e+54], t$95$2, If[LessEqual[t, 1.1e+69], t$95$1, If[LessEqual[t, 3.4e+92], t$95$2, If[LessEqual[t, 2.1e+201], t$95$1, N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 5: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-118} \lor \neg \left(x \leq 1.04 \cdot 10^{-36}\right) \land x \leq 4.4 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.4e-33)
   x
   (if (or (<= x 1.4e-118) (and (not (<= x 1.04e-36)) (<= x 4.4e+19)))
     (* t (- (/ y a)))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e-33) {
		tmp = x;
	} else if ((x <= 1.4e-118) || (!(x <= 1.04e-36) && (x <= 4.4e+19))) {
		tmp = 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 (x <= (-2.4d-33)) then
        tmp = x
    else if ((x <= 1.4d-118) .or. (.not. (x <= 1.04d-36)) .and. (x <= 4.4d+19)) then
        tmp = 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 (x <= -2.4e-33) {
		tmp = x;
	} else if ((x <= 1.4e-118) || (!(x <= 1.04e-36) && (x <= 4.4e+19))) {
		tmp = t * -(y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.4e-33:
		tmp = x
	elif (x <= 1.4e-118) or (not (x <= 1.04e-36) and (x <= 4.4e+19)):
		tmp = t * -(y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.4e-33)
		tmp = x;
	elseif ((x <= 1.4e-118) || (!(x <= 1.04e-36) && (x <= 4.4e+19)))
		tmp = Float64(t * Float64(-Float64(y / a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.4e-33)
		tmp = x;
	elseif ((x <= 1.4e-118) || (~((x <= 1.04e-36)) && (x <= 4.4e+19)))
		tmp = t * -(y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.4e-33], x, If[Or[LessEqual[x, 1.4e-118], And[N[Not[LessEqual[x, 1.04e-36]], $MachinePrecision], LessEqual[x, 4.4e+19]]], N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision], x]]

Derivation

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

Alternative 6: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+51} \lor \neg \left(z \leq 1.05 \cdot 10^{-15}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.2e+51) (not (<= z 1.05e-15)))
   (+ x (* z (/ y a)))
   (- x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e+51) || !(z <= 1.05e-15)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (y * (t / 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 ((z <= (-6.2d+51)) .or. (.not. (z <= 1.05d-15))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (y * (t / 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 ((z <= -6.2e+51) || !(z <= 1.05e-15)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.2e+51) or not (z <= 1.05e-15):
		tmp = x + (z * (y / a))
	else:
		tmp = x - (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.2e+51) || !(z <= 1.05e-15))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.2e+51) || ~((z <= 1.05e-15)))
		tmp = x + (z * (y / a));
	else
		tmp = x - (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.2e+51], N[Not[LessEqual[z, 1.05e-15]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-38} \lor \neg \left(t \leq 1.15 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e-38) (not (<= t 1.15e-10)))
   (- x (/ t (/ a y)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e-38) || !(t <= 1.15e-10)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (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 ((t <= (-8d-38)) .or. (.not. (t <= 1.15d-10))) then
        tmp = x - (t / (a / y))
    else
        tmp = x + (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 ((t <= -8e-38) || !(t <= 1.15e-10)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e-38) or not (t <= 1.15e-10):
		tmp = x - (t / (a / y))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e-38) || !(t <= 1.15e-10))
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e-38) || ~((t <= 1.15e-10)))
		tmp = x - (t / (a / y));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e-38], N[Not[LessEqual[t, 1.15e-10]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.9 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.9e-38)
   (- x (/ (* t y) a))
   (if (<= t 1.14e-10) (+ x (* z (/ y a))) (- x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.9e-38) {
		tmp = x - ((t * y) / a);
	} else if (t <= 1.14e-10) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (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) :: tmp
    if (t <= (-7.9d-38)) then
        tmp = x - ((t * y) / a)
    else if (t <= 1.14d-10) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (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 tmp;
	if (t <= -7.9e-38) {
		tmp = x - ((t * y) / a);
	} else if (t <= 1.14e-10) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.9e-38:
		tmp = x - ((t * y) / a)
	elif t <= 1.14e-10:
		tmp = x + (z * (y / a))
	else:
		tmp = x - (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.9e-38)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	elseif (t <= 1.14e-10)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.9e-38)
		tmp = x - ((t * y) / a);
	elseif (t <= 1.14e-10)
		tmp = x + (z * (y / a));
	else
		tmp = x - (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.9e-38], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.14e-10], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 93.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.8e+120) (+ x (/ y (/ a (- z t)))) (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.8e+120) {
		tmp = x + (y / (a / (z - t)));
	} 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) :: tmp
    if (t <= 4.8d+120) then
        tmp = x + (y / (a / (z - t)))
    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 tmp;
	if (t <= 4.8e+120) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.8e+120:
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.8e+120)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 4.8e+120)
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.8e+120], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 97.4% 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 11: 39.8% 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: 99.3% 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 2024008 
(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)))