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

Percentage Accurate: 93.3% → 97.6%

Time: 8.3s

Alternatives: 10

Speedup: 1.0×

• 25.4% 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: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / a) * (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. associate-*l/ 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 2: 93.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-260} \lor \neg \left(y \leq 6 \cdot 10^{-177}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.28e-260) (not (<= y 6e-177)))
   (- x (* y (/ (- z t) a)))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.28e-260) || !(y <= 6e-177)) {
		tmp = x - (y * ((z - t) / 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 ((y <= (-1.28d-260)) .or. (.not. (y <= 6d-177))) then
        tmp = x - (y * ((z - t) / 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 ((y <= -1.28e-260) || !(y <= 6e-177)) {
		tmp = x - (y * ((z - t) / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.28e-260) or not (y <= 6e-177):
		tmp = x - (y * ((z - t) / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.28e-260) || !(y <= 6e-177))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.28e-260) || ~((y <= 6e-177)))
		tmp = x - (y * ((z - t) / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.28e-260], N[Not[LessEqual[y, 6e-177]], $MachinePrecision]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.28000000000000002e-260 or 6.00000000000000015e-177 < y

   1. Initial program 87.0%

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

      1. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   if -1.28000000000000002e-260 < y < 6.00000000000000015e-177

   1. Initial program 99.8%

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

      1. associate-*r/ 60.9%

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

   3. Simplified 60.9%

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

   4. Taylor expanded in z around inf 86.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-260} \lor \neg \left(y \leq 6 \cdot 10^{-177}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+48} \lor \neg \left(t \leq 4.2 \cdot 10^{+94}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+48) (not (<= t 4.2e+94)))
   (+ x (/ t (/ a y)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+48) || !(t <= 4.2e+94)) {
		tmp = x + (t / (a / y));
	} 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 <= (-1.4d+48)) .or. (.not. (t <= 4.2d+94))) then
        tmp = x + (t / (a / y))
    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 <= -1.4e+48) || !(t <= 4.2e+94)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+48) or not (t <= 4.2e+94):
		tmp = x + (t / (a / y))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+48) || !(t <= 4.2e+94))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	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 <= -1.4e+48) || ~((t <= 4.2e+94)))
		tmp = x + (t / (a / y));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+48], N[Not[LessEqual[t, 4.2e+94]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000006e48 or 4.19999999999999979e94 < t

   1. Initial program 83.1%

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

      1. associate-*r/ 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-*l/ 86.9%

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

      3. distribute-rgt-neg-out 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around 0 74.8%

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

      1. associate-/l* 78.0%

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

      2. +-commutative 78.0%

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

      3. associate-/l* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-/l* 86.9%

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

   9. Simplified 86.9%

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

   if -1.40000000000000006e48 < t < 4.19999999999999979e94

   1. Initial program 92.6%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 87.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+48} \lor \neg \left(t \leq 4.2 \cdot 10^{+94}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 4: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+49} \lor \neg \left(t \leq 7.4 \cdot 10^{+92}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e+49) (not (<= t 7.4e+92)))
   (+ x (/ t (/ a y)))
   (- x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e+49) || !(t <= 7.4e+92)) {
		tmp = x + (t / (a / y));
	} 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) :: tmp
    if ((t <= (-3.4d+49)) .or. (.not. (t <= 7.4d+92))) then
        tmp = x + (t / (a / y))
    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 tmp;
	if ((t <= -3.4e+49) || !(t <= 7.4e+92)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.4e+49) or not (t <= 7.4e+92):
		tmp = x + (t / (a / y))
	else:
		tmp = x - ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.4e+49) || !(t <= 7.4e+92))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x - Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.4e+49) || ~((t <= 7.4e+92)))
		tmp = x + (t / (a / y));
	else
		tmp = x - ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.4e+49], N[Not[LessEqual[t, 7.4e+92]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e49 or 7.39999999999999997e92 < t

   1. Initial program 83.1%

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

      1. associate-*r/ 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-*l/ 86.9%

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

      3. distribute-rgt-neg-out 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around 0 74.8%

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

      1. associate-/l* 78.0%

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

      2. +-commutative 78.0%

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

      3. associate-/l* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-/l* 86.9%

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

   9. Simplified 86.9%

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

   if -3.4000000000000001e49 < t < 7.39999999999999997e92

   1. Initial program 92.6%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

   6. Simplified 91.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+49} \lor \neg \left(t \leq 7.4 \cdot 10^{+92}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 5: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e+46)
   (+ x (* (/ y a) t))
   (if (<= t 1.8e+92) (- x (* (/ y a) z)) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e+46) {
		tmp = x + ((y / a) * t);
	} else if (t <= 1.8e+92) {
		tmp = x - ((y / a) * z);
	} 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 <= (-7.5d+46)) then
        tmp = x + ((y / a) * t)
    else if (t <= 1.8d+92) then
        tmp = x - ((y / a) * z)
    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 <= -7.5e+46) {
		tmp = x + ((y / a) * t);
	} else if (t <= 1.8e+92) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e+46:
		tmp = x + ((y / a) * t)
	elif t <= 1.8e+92:
		tmp = x - ((y / a) * z)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e+46)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	elseif (t <= 1.8e+92)
		tmp = Float64(x - Float64(Float64(y / a) * z));
	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 <= -7.5e+46)
		tmp = x + ((y / a) * t);
	elseif (t <= 1.8e+92)
		tmp = x - ((y / a) * z);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e+46], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+92], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5000000000000003e46

   1. Initial program 86.3%

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

      1. associate-*r/ 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. associate-*l/ 86.7%

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

      3. distribute-rgt-neg-out 86.7%

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

   6. Simplified 86.7%

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

   if -7.5000000000000003e46 < t < 1.8e92

   1. Initial program 92.6%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   if 1.8e92 < t

   1. Initial program 80.3%

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

      1. associate-*r/ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in z around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. associate-*l/ 87.2%

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

      3. distribute-rgt-neg-out 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in x around 0 72.8%

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

      1. associate-/l* 77.8%

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

      2. +-commutative 77.8%

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

      3. associate-/l* 72.8%

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

      4. *-commutative 72.8%

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

      5. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+27} \lor \neg \left(t \leq 7.8 \cdot 10^{+72}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+27) (not (<= t 7.8e+72))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+27) || !(t <= 7.8e+72)) {
		tmp = y * (t / 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 ((t <= (-2.8d+27)) .or. (.not. (t <= 7.8d+72))) then
        tmp = y * (t / 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 ((t <= -2.8e+27) || !(t <= 7.8e+72)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+27) or not (t <= 7.8e+72):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+27) || !(t <= 7.8e+72))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+27) || ~((t <= 7.8e+72)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+27], N[Not[LessEqual[t, 7.8e+72]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.7999999999999999e27 or 7.79999999999999984e72 < t

   1. Initial program 83.5%

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

      1. associate-*r/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-*l/ 85.2%

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

      3. distribute-rgt-neg-out 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in x around 0 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 61.8%

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

   9. Simplified 61.8%

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

       1. associate-/r/ 54.2%

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

   11. Applied egg-rr 54.2%

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

   if -2.7999999999999999e27 < t < 7.79999999999999984e72

   1. Initial program 92.8%

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

      1. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-*l/ 53.6%

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

      3. distribute-rgt-neg-out 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in x around inf 44.7%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+27} \lor \neg \left(t \leq 7.8 \cdot 10^{+72}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+27} \lor \neg \left(t \leq 1.42 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+27) (not (<= t 1.42e+72))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+27) || !(t <= 1.42e+72)) {
		tmp = (y / a) * t;
	} 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 ((t <= (-2.8d+27)) .or. (.not. (t <= 1.42d+72))) then
        tmp = (y / a) * t
    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 ((t <= -2.8e+27) || !(t <= 1.42e+72)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+27) or not (t <= 1.42e+72):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+27) || !(t <= 1.42e+72))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+27) || ~((t <= 1.42e+72)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+27], N[Not[LessEqual[t, 1.42e+72]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.7999999999999999e27 or 1.41999999999999997e72 < t

   1. Initial program 83.5%

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

      1. associate-*r/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-*l/ 85.2%

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

      3. distribute-rgt-neg-out 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in x around 0 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 61.8%

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

   9. Simplified 61.8%

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

       1. div-inv 61.8%

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

       2. clear-num 61.8%

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

       3. *-commutative 61.8%

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

   11. Applied egg-rr 61.8%

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

   if -2.7999999999999999e27 < t < 1.41999999999999997e72

   1. Initial program 92.8%

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

      1. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-*l/ 53.6%

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

      3. distribute-rgt-neg-out 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in x around inf 44.7%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+27} \lor \neg \left(t \leq 1.42 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.4e+22) (* (/ y a) t) (if (<= t 5.8e+71) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.4e+22) {
		tmp = (y / a) * t;
	} else if (t <= 5.8e+71) {
		tmp = x;
	} else {
		tmp = 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 <= (-7.4d+22)) then
        tmp = (y / a) * t
    else if (t <= 5.8d+71) then
        tmp = x
    else
        tmp = 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 <= -7.4e+22) {
		tmp = (y / a) * t;
	} else if (t <= 5.8e+71) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.4e+22:
		tmp = (y / a) * t
	elif t <= 5.8e+71:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.4e+22)
		tmp = Float64(Float64(y / a) * t);
	elseif (t <= 5.8e+71)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.4e+22)
		tmp = (y / a) * t;
	elseif (t <= 5.8e+71)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.4e+22], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 5.8e+71], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.3999999999999996e22

   1. Initial program 85.5%

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

      1. associate-*r/ 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate-*l/ 84.0%

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

      3. distribute-rgt-neg-out 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in x around 0 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-/l* 60.3%

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

   9. Simplified 60.3%

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

       1. div-inv 60.3%

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

       2. clear-num 60.4%

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

       3. *-commutative 60.4%

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

   11. Applied egg-rr 60.4%

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

   if -7.3999999999999996e22 < t < 5.80000000000000014e71

   1. Initial program 92.8%

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

      1. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-*l/ 53.6%

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

      3. distribute-rgt-neg-out 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in x around inf 44.7%

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

   if 5.80000000000000014e71 < t

   1. Initial program 81.6%

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

      1. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-*l/ 86.3%

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

      3. distribute-rgt-neg-out 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in x around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-/l* 63.2%

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

   9. Simplified 63.2%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 71.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (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 + (t / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. associate-*r/ 91.1%

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

3. Simplified 91.1%

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

4. Taylor expanded in z around 0 61.2%

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

   1. mul-1-neg 61.2%

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

   2. associate-*l/ 67.1%

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

   3. distribute-rgt-neg-out 67.1%

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

6. Simplified 67.1%

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

7. Taylor expanded in x around 0 61.2%

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

   1. associate-/l* 62.5%

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

   2. +-commutative 62.5%

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

   3. associate-/l* 61.2%

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

   4. *-commutative 61.2%

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

   5. associate-/l* 67.1%

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

9. Simplified 67.1%

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

10. Final simplification 67.1%

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

Alternative 10: 40.5% 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 88.8%

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

   1. associate-*r/ 91.1%

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

3. Simplified 91.1%

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

4. Taylor expanded in z around 0 61.2%

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

   1. mul-1-neg 61.2%

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

   2. associate-*l/ 67.1%

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

   3. distribute-rgt-neg-out 67.1%

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

6. Simplified 67.1%

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

7. Taylor expanded in x around inf 36.0%

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

8. Final simplification 36.0%

   \[\leadsto x \]

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 2023229 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))