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

Percentage Accurate: 93.3% → 98.1%

Time: 10.0s

Alternatives: 11

Speedup: 1.0×

• 25.0% 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: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+275} \lor \neg \left(t_1 \leq 2 \cdot 10^{+285}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -4e+275) (not (<= t_1 2e+285)))
     (* (- z t) (/ y a))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -4e+275) || !(t_1 <= 2e+285)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (t_1 / 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 = y * (z - t)
    if ((t_1 <= (-4d+275)) .or. (.not. (t_1 <= 2d+285))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (t_1 / 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 = y * (z - t);
	double tmp;
	if ((t_1 <= -4e+275) || !(t_1 <= 2e+285)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -4e+275) or not (t_1 <= 2e+285):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -4e+275) || !(t_1 <= 2e+285))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -4e+275) || ~((t_1 <= 2e+285)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+275], N[Not[LessEqual[t$95$1, 2e+285]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -3.99999999999999984e275 or 2e285 < (*.f64 y (-.f64 z t))

   1. Initial program 70.2%

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

   2. Taylor expanded in x around 0 70.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   3. Step-by-step derivation

      1. associate-*l/ 96.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   4. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   if -3.99999999999999984e275 < (*.f64 y (-.f64 z t)) < 2e285

   1. Initial program 98.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -4 \cdot 10^{+275} \lor \neg \left(y \cdot \left(z - t\right) \leq 2 \cdot 10^{+285}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]

Alternative 2: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-26} \lor \neg \left(t_1 \leq 2 \cdot 10^{+162}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -2e-26) (not (<= t_1 2e+162)))
     (* (- z t) (/ y a))
     (+ x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e-26) || !(t_1 <= 2e+162)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y / (a / z));
	}
	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 = (y * (z - t)) / a
    if ((t_1 <= (-2d-26)) .or. (.not. (t_1 <= 2d+162))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e-26) || !(t_1 <= 2e+162)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -2e-26) or not (t_1 <= 2e+162):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -2e-26) || !(t_1 <= 2e+162))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if ((t_1 <= -2e-26) || ~((t_1 <= 2e+162)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-26], N[Not[LessEqual[t$95$1, 2e+162]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e-26 or 1.9999999999999999e162 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 84.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   3. Step-by-step derivation

      1. associate-*l/ 94.3%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   4. Applied egg-rr 94.3%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   if -2.0000000000000001e-26 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.9999999999999999e162

   1. Initial program 97.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

      2. div-inv 92.8%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{1}{a}\right)} \cdot \left(z - t\right) \]

      3. associate-*l* 97.5%

         \[\leadsto x + \color{blue}{y \cdot \left(\frac{1}{a} \cdot \left(z - t\right)\right)} \]

   3. Applied egg-rr 97.5%

      \[\leadsto x + \color{blue}{y \cdot \left(\frac{1}{a} \cdot \left(z - t\right)\right)} \]

   4. Taylor expanded in z around inf 84.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 84.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   6. Simplified 84.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{-26} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+162}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 3: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-t}{a}\\ \mathbf{if}\;a \leq -1.3:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.00385:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t) a))))
   (if (<= a -1.3)
     x
     (if (<= a -8.5e-209)
       (/ (* y z) a)
       (if (<= a -5e-256)
         t_1
         (if (<= a 0.00385) (* z (/ y a)) (if (<= a 1.12e+33) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / a);
	double tmp;
	if (a <= -1.3) {
		tmp = x;
	} else if (a <= -8.5e-209) {
		tmp = (y * z) / a;
	} else if (a <= -5e-256) {
		tmp = t_1;
	} else if (a <= 0.00385) {
		tmp = z * (y / a);
	} else if (a <= 1.12e+33) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (-t / a)
    if (a <= (-1.3d0)) then
        tmp = x
    else if (a <= (-8.5d-209)) then
        tmp = (y * z) / a
    else if (a <= (-5d-256)) then
        tmp = t_1
    else if (a <= 0.00385d0) then
        tmp = z * (y / a)
    else if (a <= 1.12d+33) then
        tmp = t_1
    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 t_1 = y * (-t / a);
	double tmp;
	if (a <= -1.3) {
		tmp = x;
	} else if (a <= -8.5e-209) {
		tmp = (y * z) / a;
	} else if (a <= -5e-256) {
		tmp = t_1;
	} else if (a <= 0.00385) {
		tmp = z * (y / a);
	} else if (a <= 1.12e+33) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-t / a)
	tmp = 0
	if a <= -1.3:
		tmp = x
	elif a <= -8.5e-209:
		tmp = (y * z) / a
	elif a <= -5e-256:
		tmp = t_1
	elif a <= 0.00385:
		tmp = z * (y / a)
	elif a <= 1.12e+33:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-t) / a))
	tmp = 0.0
	if (a <= -1.3)
		tmp = x;
	elseif (a <= -8.5e-209)
		tmp = Float64(Float64(y * z) / a);
	elseif (a <= -5e-256)
		tmp = t_1;
	elseif (a <= 0.00385)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 1.12e+33)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-t / a);
	tmp = 0.0;
	if (a <= -1.3)
		tmp = x;
	elseif (a <= -8.5e-209)
		tmp = (y * z) / a;
	elseif (a <= -5e-256)
		tmp = t_1;
	elseif (a <= 0.00385)
		tmp = z * (y / a);
	elseif (a <= 1.12e+33)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3], x, If[LessEqual[a, -8.5e-209], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -5e-256], t$95$1, If[LessEqual[a, 0.00385], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+33], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.30000000000000004 or 1.12e33 < a

   1. Initial program 85.3%

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

   2. Taylor expanded in x around inf 63.6%

      \[\leadsto \color{blue}{x} \]

   if -1.30000000000000004 < a < -8.5e-209

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around inf 53.6%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]

   if -8.5e-209 < a < -5e-256 or 0.0038500000000000001 < a < 1.12e33

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around 0 78.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.5%

         \[\leadsto \color{blue}{-\frac{t \cdot y}{a}} \]

      2. associate-*l/ 74.4%

         \[\leadsto -\color{blue}{\frac{t}{a} \cdot y} \]

      3. distribute-rgt-neg-in 74.4%

         \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(-y\right)} \]

   5. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(-y\right)} \]

   if -5e-256 < a < 0.0038500000000000001

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around inf 55.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 56.9%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 56.9%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;a \leq 0.00385:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;a \leq -15:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-208}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.0045:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= a -15.0)
     x
     (if (<= a -8e-208)
       (/ (* y z) a)
       (if (<= a -2.1e-260)
         t_1
         (if (<= a 0.0045) (* z (/ y a)) (if (<= a 1.25e+33) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (a <= -15.0) {
		tmp = x;
	} else if (a <= -8e-208) {
		tmp = (y * z) / a;
	} else if (a <= -2.1e-260) {
		tmp = t_1;
	} else if (a <= 0.0045) {
		tmp = z * (y / a);
	} else if (a <= 1.25e+33) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (a <= (-15.0d0)) then
        tmp = x
    else if (a <= (-8d-208)) then
        tmp = (y * z) / a
    else if (a <= (-2.1d-260)) then
        tmp = t_1
    else if (a <= 0.0045d0) then
        tmp = z * (y / a)
    else if (a <= 1.25d+33) then
        tmp = t_1
    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 t_1 = t * (-y / a);
	double tmp;
	if (a <= -15.0) {
		tmp = x;
	} else if (a <= -8e-208) {
		tmp = (y * z) / a;
	} else if (a <= -2.1e-260) {
		tmp = t_1;
	} else if (a <= 0.0045) {
		tmp = z * (y / a);
	} else if (a <= 1.25e+33) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if a <= -15.0:
		tmp = x
	elif a <= -8e-208:
		tmp = (y * z) / a
	elif a <= -2.1e-260:
		tmp = t_1
	elif a <= 0.0045:
		tmp = z * (y / a)
	elif a <= 1.25e+33:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (a <= -15.0)
		tmp = x;
	elseif (a <= -8e-208)
		tmp = Float64(Float64(y * z) / a);
	elseif (a <= -2.1e-260)
		tmp = t_1;
	elseif (a <= 0.0045)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 1.25e+33)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (a <= -15.0)
		tmp = x;
	elseif (a <= -8e-208)
		tmp = (y * z) / a;
	elseif (a <= -2.1e-260)
		tmp = t_1;
	elseif (a <= 0.0045)
		tmp = z * (y / a);
	elseif (a <= 1.25e+33)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -15.0], x, If[LessEqual[a, -8e-208], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -2.1e-260], t$95$1, If[LessEqual[a, 0.0045], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+33], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -15 or 1.24999999999999993e33 < a

   1. Initial program 85.3%

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

   2. Taylor expanded in x around inf 63.6%

      \[\leadsto \color{blue}{x} \]

   if -15 < a < -8.0000000000000008e-208

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around inf 53.6%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]

   if -8.0000000000000008e-208 < a < -2.10000000000000005e-260 or 0.00449999999999999966 < a < 1.24999999999999993e33

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a}} \]
   3. Step-by-step derivation

      1. mul-1-neg 86.9%

         \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a}\right)} \]

      2. associate-*l/ 82.6%

         \[\leadsto x + \left(-\color{blue}{\frac{t}{a} \cdot y}\right) \]

      3. unsub-neg 82.6%

         \[\leadsto \color{blue}{x - \frac{t}{a} \cdot y} \]

      4. associate-*l/ 86.9%

         \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]

      5. *-commutative 86.9%

         \[\leadsto x - \frac{\color{blue}{y \cdot t}}{a} \]

      6. associate-/l* 82.6%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{t}}} \]

   4. Simplified 82.6%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 87.0%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot t} \]

   6. Applied egg-rr 87.0%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot t} \]

   7. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 78.6%

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \frac{y}{a}\right)} \]

      2. associate-*l* 78.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \frac{y}{a}} \]

      3. neg-mul-1 78.6%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \frac{y}{a} \]

      4. *-commutative 78.6%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]

   9. Simplified 78.6%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]

   if -2.10000000000000005e-260 < a < 0.00449999999999999966

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around inf 55.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 56.9%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 56.9%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -15:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-208}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 0.0045:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-38} \lor \neg \left(a \leq 1.95 \cdot 10^{-75} \lor \neg \left(a \leq 1.6 \cdot 10^{-20}\right) \land a \leq 5.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e-38)
         (not (or (<= a 1.95e-75) (and (not (<= a 1.6e-20)) (<= a 5.5e+31)))))
   (+ x (* z (/ y a)))
   (* (- z t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e-38) || !((a <= 1.95e-75) || (!(a <= 1.6e-20) && (a <= 5.5e+31)))) {
		tmp = x + (z * (y / 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 ((a <= (-7d-38)) .or. (.not. (a <= 1.95d-75) .or. (.not. (a <= 1.6d-20)) .and. (a <= 5.5d+31))) then
        tmp = x + (z * (y / 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 ((a <= -7e-38) || !((a <= 1.95e-75) || (!(a <= 1.6e-20) && (a <= 5.5e+31)))) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e-38) or not ((a <= 1.95e-75) or (not (a <= 1.6e-20) and (a <= 5.5e+31))):
		tmp = x + (z * (y / a))
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7e-38) || !((a <= 1.95e-75) || (!(a <= 1.6e-20) && (a <= 5.5e+31))))
		tmp = Float64(x + Float64(z * Float64(y / 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 ((a <= -7e-38) || ~(((a <= 1.95e-75) || (~((a <= 1.6e-20)) && (a <= 5.5e+31)))))
		tmp = x + (z * (y / a));
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e-38], N[Not[Or[LessEqual[a, 1.95e-75], And[N[Not[LessEqual[a, 1.6e-20]], $MachinePrecision], LessEqual[a, 5.5e+31]]]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.0000000000000003e-38 or 1.9500000000000001e-75 < a < 1.59999999999999985e-20 or 5.50000000000000002e31 < a

   1. Initial program 87.9%

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

   2. Taylor expanded in z around inf 76.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*l/ 21.0%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 21.0%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   4. Simplified 79.6%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a}} \]

   if -7.0000000000000003e-38 < a < 1.9500000000000001e-75 or 1.59999999999999985e-20 < a < 5.50000000000000002e31

   1. Initial program 97.4%

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

   2. Taylor expanded in x around 0 87.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   3. Step-by-step derivation

      1. associate-*l/ 88.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   4. Applied egg-rr 88.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-38} \lor \neg \left(a \leq 1.95 \cdot 10^{-75} \lor \neg \left(a \leq 1.6 \cdot 10^{-20}\right) \land a \leq 5.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+151} \lor \neg \left(a \leq -25\right) \land a \leq 1.15 \cdot 10^{+43}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+184)
   x
   (if (or (<= a -4.8e+151) (and (not (<= a -25.0)) (<= a 1.15e+43)))
     (* (- z t) (/ y a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+184) {
		tmp = x;
	} else if ((a <= -4.8e+151) || (!(a <= -25.0) && (a <= 1.15e+43))) {
		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 <= (-1.35d+184)) then
        tmp = x
    else if ((a <= (-4.8d+151)) .or. (.not. (a <= (-25.0d0))) .and. (a <= 1.15d+43)) 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 <= -1.35e+184) {
		tmp = x;
	} else if ((a <= -4.8e+151) || (!(a <= -25.0) && (a <= 1.15e+43))) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+184:
		tmp = x
	elif (a <= -4.8e+151) or (not (a <= -25.0) and (a <= 1.15e+43)):
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+184)
		tmp = x;
	elseif ((a <= -4.8e+151) || (!(a <= -25.0) && (a <= 1.15e+43)))
		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 <= -1.35e+184)
		tmp = x;
	elseif ((a <= -4.8e+151) || (~((a <= -25.0)) && (a <= 1.15e+43)))
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+184], x, If[Or[LessEqual[a, -4.8e+151], And[N[Not[LessEqual[a, -25.0]], $MachinePrecision], LessEqual[a, 1.15e+43]]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e184 or -4.8000000000000002e151 < a < -25 or 1.1500000000000001e43 < a

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 67.7%

      \[\leadsto \color{blue}{x} \]

   if -1.35e184 < a < -4.8000000000000002e151 or -25 < a < 1.1500000000000001e43

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 78.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   3. Step-by-step derivation

      1. associate-*l/ 81.3%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   4. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+151} \lor \neg \left(a \leq -25\right) \land a \leq 1.15 \cdot 10^{+43}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(\frac{1}{a} \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e-11)
   (+ x (* y (* (/ 1.0 a) (- z t))))
   (+ x (/ (- z t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-11) {
		tmp = x + (y * ((1.0 / a) * (z - t)));
	} else {
		tmp = x + ((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) :: tmp
    if (a <= (-3d-11)) then
        tmp = x + (y * ((1.0d0 / a) * (z - t)))
    else
        tmp = x + ((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 tmp;
	if (a <= -3e-11) {
		tmp = x + (y * ((1.0 / a) * (z - t)));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e-11:
		tmp = x + (y * ((1.0 / a) * (z - t)))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e-11)
		tmp = Float64(x + Float64(y * Float64(Float64(1.0 / a) * Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e-11)
		tmp = x + (y * ((1.0 / a) * (z - t)));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e-11], N[(x + N[(y * N[(N[(1.0 / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3e-11

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

      2. div-inv 93.6%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{1}{a}\right)} \cdot \left(z - t\right) \]

      3. associate-*l* 99.9%

         \[\leadsto x + \color{blue}{y \cdot \left(\frac{1}{a} \cdot \left(z - t\right)\right)} \]

   3. Applied egg-rr 99.9%

      \[\leadsto x + \color{blue}{y \cdot \left(\frac{1}{a} \cdot \left(z - t\right)\right)} \]

   if -3e-11 < a

   1. Initial program 94.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a} \]

      2. associate-/l* 96.6%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   3. Simplified 96.6%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(\frac{1}{a} \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0275:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.065:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0275) x (if (<= a 0.065) (* z (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0275) {
		tmp = x;
	} else if (a <= 0.065) {
		tmp = z * (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 <= (-0.0275d0)) then
        tmp = x
    else if (a <= 0.065d0) then
        tmp = z * (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 <= -0.0275) {
		tmp = x;
	} else if (a <= 0.065) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0275:
		tmp = x
	elif a <= 0.065:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0275)
		tmp = x;
	elseif (a <= 0.065)
		tmp = Float64(z * 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 <= -0.0275)
		tmp = x;
	elseif (a <= 0.065)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0275], x, If[LessEqual[a, 0.065], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -0.0275000000000000001 or 0.065000000000000002 < a

   1. Initial program 86.5%

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

   2. Taylor expanded in x around inf 60.2%

      \[\leadsto \color{blue}{x} \]

   if -0.0275000000000000001 < a < 0.065000000000000002

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 81.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around inf 51.0%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 51.3%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 51.3%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0275:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.065:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.052:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9) x (if (<= a 0.052) (/ z (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9) {
		tmp = x;
	} else if (a <= 0.052) {
		tmp = z / (a / y);
	} 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 <= (-1.9d0)) then
        tmp = x
    else if (a <= 0.052d0) then
        tmp = z / (a / y)
    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 <= -1.9) {
		tmp = x;
	} else if (a <= 0.052) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9:
		tmp = x
	elif a <= 0.052:
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9)
		tmp = x;
	elseif (a <= 0.052)
		tmp = Float64(z / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9)
		tmp = x;
	elseif (a <= 0.052)
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9], x, If[LessEqual[a, 0.052], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999 or 0.0519999999999999976 < a

   1. Initial program 86.5%

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

   2. Taylor expanded in x around inf 60.2%

      \[\leadsto \color{blue}{x} \]

   if -1.8999999999999999 < a < 0.0519999999999999976

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 81.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]

   3. Taylor expanded in z around inf 51.0%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 51.3%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 51.3%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 51.3%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 51.6%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{y}}} \]

   7. Applied egg-rr 51.6%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.052:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 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

1. Initial program 92.4%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
2. Step-by-step derivation

   1. *-commutative 92.4%

      \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a} \]

   2. associate-/l* 95.8%

      \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

3. Simplified 95.8%

   \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a}{y}}} \]

4. Final simplification 95.8%

   \[\leadsto x + \frac{z - t}{\frac{a}{y}} \]

Alternative 11: 39.1% 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

1. Initial program 92.4%

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

2. Taylor expanded in x around inf 37.5%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 37.5%

   \[\leadsto x \]

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 2023318 
(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)))