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

Percentage Accurate: 93.4% → 96.9%

Time: 8.3s

Alternatives: 8

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% 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: 96.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{\frac{\frac{a}{y}}{z - t}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ 1.0 (/ (/ a y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (1.0 / ((a / y) / (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 + (1.0d0 / ((a / y) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (1.0 / ((a / y) / (z - t)));
}

Python

def code(x, y, z, t, a):
	return x + (1.0 / ((a / y) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(1.0 / Float64(Float64(a / y) / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (1.0 / ((a / y) / (z - t)));
end

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. associate-*l/ 97.4%

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

3. Simplified 97.4%

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

   1. associate-*l/ 94.8%

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

   2. clear-num 94.8%

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

   3. associate-/r* 97.5%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{y}}{z - t}}} \]

5. Applied egg-rr 97.5%

   \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{y}}{z - t}}} \]

6. Final simplification 97.5%

   \[\leadsto x + \frac{1}{\frac{\frac{a}{y}}{z - t}} \]

Alternative 2: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+145} \lor \neg \left(t \leq 3.6 \cdot 10^{+105}\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e+145) (not (<= t 3.6e+105)))
   (* y (/ (- t) a))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+145) || !(t <= 3.6e+105)) {
		tmp = y * (-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 ((t <= (-1.1d+145)) .or. (.not. (t <= 3.6d+105))) then
        tmp = y * (-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 ((t <= -1.1e+145) || !(t <= 3.6e+105)) {
		tmp = y * (-t / a);
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e+145) or not (t <= 3.6e+105):
		tmp = y * (-t / a)
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e+145) || !(t <= 3.6e+105))
		tmp = Float64(y * Float64(Float64(-t) / a));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e+145) || ~((t <= 3.6e+105)))
		tmp = y * (-t / a);
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e+145], N[Not[LessEqual[t, 3.6e+105]], $MachinePrecision]], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.10000000000000004e145 or 3.5999999999999999e105 < t

   1. Initial program 91.5%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

      3. associate-*r/ 84.7%

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

   6. Simplified 84.7%

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

      1. associate-*r/ 80.6%

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

      2. clear-num 80.5%

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

      3. add-sqr-sqrt 49.9%

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

      4. sqrt-unprod 34.1%

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

      5. sqr-neg 34.1%

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

      6. sqrt-unprod 9.1%

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

      7. add-sqr-sqrt 23.0%

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

      8. *-commutative 23.0%

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

      9. add-sqr-sqrt 9.1%

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

      10. sqrt-unprod 34.1%

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

      11. sqr-neg 34.1%

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

      12. sqrt-unprod 49.9%

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

      13. add-sqr-sqrt 80.5%

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

   8. Applied egg-rr 80.5%

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

   9. Taylor expanded in x around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. associate-*l/ 67.5%

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

       3. distribute-rgt-neg-in 67.5%

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

   11. Simplified 67.5%

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

   if -1.10000000000000004e145 < t < 3.5999999999999999e105

   1. Initial program 96.6%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

      1. associate-*l/ 96.6%

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

      2. clear-num 96.5%

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

      3. associate-/r* 98.6%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{y}}{z - t}}} \]

   5. Applied egg-rr 98.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{y}}{z - t}}} \]

   6. Taylor expanded in z around inf 80.7%

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

      1. associate-*r/ 81.2%

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

   8. Simplified 81.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+145} \lor \neg \left(t \leq 3.6 \cdot 10^{+105}\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 3: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+144} \lor \neg \left(t \leq 9 \cdot 10^{+99}\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e+144) (not (<= t 9e+99)))
   (* y (/ (- t) a))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+144) || !(t <= 9e+99)) {
		tmp = y * (-t / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.5d+144)) .or. (.not. (t <= 9d+99))) then
        tmp = y * (-t / a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+144) || !(t <= 9e+99)) {
		tmp = y * (-t / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.5e+144) or not (t <= 9e+99):
		tmp = y * (-t / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e+144) || !(t <= 9e+99))
		tmp = Float64(y * Float64(Float64(-t) / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.5e+144) || ~((t <= 9e+99)))
		tmp = y * (-t / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.5e+144], N[Not[LessEqual[t, 9e+99]], $MachinePrecision]], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000006e144 or 8.9999999999999999e99 < t

   1. Initial program 91.5%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

      3. associate-*r/ 84.7%

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

   6. Simplified 84.7%

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

      1. associate-*r/ 80.6%

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

      2. clear-num 80.5%

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

      3. add-sqr-sqrt 49.9%

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

      4. sqrt-unprod 34.1%

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

      5. sqr-neg 34.1%

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

      6. sqrt-unprod 9.1%

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

      7. add-sqr-sqrt 23.0%

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

      8. *-commutative 23.0%

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

      9. add-sqr-sqrt 9.1%

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

      10. sqrt-unprod 34.1%

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

      11. sqr-neg 34.1%

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

      12. sqrt-unprod 49.9%

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

      13. add-sqr-sqrt 80.5%

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

   8. Applied egg-rr 80.5%

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

   9. Taylor expanded in x around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. associate-*l/ 67.5%

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

       3. distribute-rgt-neg-in 67.5%

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

   11. Simplified 67.5%

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

   if -7.5000000000000006e144 < t < 8.9999999999999999e99

   1. Initial program 96.6%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around 0 80.7%

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

      1. +-commutative 80.7%

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

      2. associate-*l/ 85.1%

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

      3. *-commutative 85.1%

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

   6. Simplified 85.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+144} \lor \neg \left(t \leq 9 \cdot 10^{+99}\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+123} \lor \neg \left(t \leq 38000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+123) (not (<= t 38000000.0)))
   (- x (* t (/ y a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+123) || !(t <= 38000000.0)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d+123)) .or. (.not. (t <= 38000000.0d0))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+123) || !(t <= 38000000.0)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+123) or not (t <= 38000000.0):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+123) || !(t <= 38000000.0))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+123) || ~((t <= 38000000.0)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+123], N[Not[LessEqual[t, 38000000.0]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999978e123 or 3.8e7 < t

   1. Initial program 92.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. associate-*r/ 84.5%

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

   6. Simplified 84.5%

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

   if -4.79999999999999978e123 < t < 3.8e7

   1. Initial program 96.2%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

   6. Simplified 87.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+123} \lor \neg \left(t \leq 38000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+123} \lor \neg \left(t \leq 26000000\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+123) (not (<= t 26000000.0)))
   (- x (/ y (/ a t)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+123) || !(t <= 26000000.0)) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d+123)) .or. (.not. (t <= 26000000.0d0))) then
        tmp = x - (y / (a / t))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+123) || !(t <= 26000000.0)) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+123) or not (t <= 26000000.0):
		tmp = x - (y / (a / t))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+123) || !(t <= 26000000.0))
		tmp = Float64(x - Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+123) || ~((t <= 26000000.0)))
		tmp = x - (y / (a / t));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+123], N[Not[LessEqual[t, 26000000.0]], $MachinePrecision]], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999978e123 or 2.6e7 < t

   1. Initial program 92.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. associate-*r/ 84.5%

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

   6. Simplified 84.5%

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

      1. associate-*r/ 81.1%

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

      2. add-cube-cbrt 80.7%

         \[\leadsto x - \frac{t \cdot y}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \]

      3. times-frac 85.0%

         \[\leadsto x - \color{blue}{\frac{t}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}}} \]

      4. add-sqr-sqrt 54.1%

         \[\leadsto x - \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      5. sqrt-unprod 42.2%

         \[\leadsto x - \frac{\color{blue}{\sqrt{t \cdot t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      6. sqr-neg 42.2%

         \[\leadsto x - \frac{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      7. sqrt-unprod 10.4%

         \[\leadsto x - \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      8. add-sqr-sqrt 29.6%

         \[\leadsto x - \frac{\color{blue}{-t}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      9. times-frac 28.7%

         \[\leadsto x - \color{blue}{\frac{\left(-t\right) \cdot y}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \]

      10. *-commutative 28.7%

          \[\leadsto x - \frac{\color{blue}{y \cdot \left(-t\right)}}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}} \]

      11. add-cube-cbrt 28.7%

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

      12. associate-/l* 29.6%

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

      13. add-sqr-sqrt 10.4%

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

      14. sqrt-unprod 43.2%

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

      15. sqr-neg 43.2%

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

      16. sqrt-unprod 55.3%

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

      17. add-sqr-sqrt 86.3%

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

   8. Applied egg-rr 86.3%

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

   if -4.79999999999999978e123 < t < 2.6e7

   1. Initial program 96.2%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

   6. Simplified 87.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+123} \lor \neg \left(t \leq 26000000\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 49.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+143} \lor \neg \left(t \leq 6000000000\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6e+143) (not (<= t 6000000000.0))) (* y (/ (- t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e+143) || !(t <= 6000000000.0)) {
		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 <= (-6d+143)) .or. (.not. (t <= 6000000000.0d0))) 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 <= -6e+143) || !(t <= 6000000000.0)) {
		tmp = y * (-t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6e+143) or not (t <= 6000000000.0):
		tmp = y * (-t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6e+143) || !(t <= 6000000000.0))
		tmp = Float64(y * Float64(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 <= -6e+143) || ~((t <= 6000000000.0)))
		tmp = y * (-t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6e+143], N[Not[LessEqual[t, 6000000000.0]], $MachinePrecision]], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.0000000000000001e143 or 6e9 < t

   1. Initial program 92.6%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. unsub-neg 80.1%

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

      3. associate-*r/ 83.7%

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

   6. Simplified 83.7%

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

      1. associate-*r/ 80.1%

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

      2. clear-num 80.0%

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

      3. add-sqr-sqrt 53.2%

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

      4. sqrt-unprod 39.5%

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

      5. sqr-neg 39.5%

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

      6. sqrt-unprod 7.9%

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

      7. add-sqr-sqrt 26.2%

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

      8. *-commutative 26.2%

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

      9. add-sqr-sqrt 7.9%

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

      10. sqrt-unprod 39.5%

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

      11. sqr-neg 39.5%

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

      12. sqrt-unprod 53.2%

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

      13. add-sqr-sqrt 80.0%

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

   8. Applied egg-rr 80.0%

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

   9. Taylor expanded in x around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*l/ 64.5%

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

       3. distribute-rgt-neg-in 64.5%

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

   11. Simplified 64.5%

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

   if -6.0000000000000001e143 < t < 6e9

   1. Initial program 96.3%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around inf 48.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+143} \lor \neg \left(t \leq 6000000000\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. associate-*l/ 97.4%

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

3. Simplified 97.4%

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

4. Final simplification 97.4%

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

Alternative 8: 39.2% 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 94.8%

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

   1. associate-*l/ 97.4%

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

3. Simplified 97.4%

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

4. Taylor expanded in x around inf 38.2%

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

5. Final simplification 38.2%

   \[\leadsto x \]

Developer target: 99.4% 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 2023275 
(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)))