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

Percentage Accurate: 92.9% → 97.5%

Time: 7.7s

Alternatives: 8

Speedup: 1.0×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 52.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-33} \lor \neg \left(z \leq 3.4 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-33) (not (<= z 3.4e+146)))
   (* (/ y a) (- z))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-33) || !(z <= 3.4e+146)) {
		tmp = (y / a) * -z;
	} 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 ((z <= (-1.15d-33)) .or. (.not. (z <= 3.4d+146))) then
        tmp = (y / a) * -z
    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 ((z <= -1.15e-33) || !(z <= 3.4e+146)) {
		tmp = (y / a) * -z;
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-33) or not (z <= 3.4e+146):
		tmp = (y / a) * -z
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-33) || !(z <= 3.4e+146))
		tmp = Float64(Float64(y / a) * Float64(-z));
	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 ((z <= -1.15e-33) || ~((z <= 3.4e+146)))
		tmp = (y / a) * -z;
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-33], N[Not[LessEqual[z, 3.4e+146]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999993e-33 or 3.39999999999999991e146 < z

   1. Initial program 84.6%

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

   5. Taylor expanded in z around inf 75.6%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

   7. Simplified 85.2%

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

      1. clear-num 85.2%

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

      2. un-div-inv 85.2%

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

   9. Applied egg-rr 85.2%

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

   10. Taylor expanded in x around 0 55.2%

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

       1. *-commutative 55.2%

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

       2. associate-*r/ 64.1%

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

       3. associate-*r* 64.1%

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

       4. neg-mul-1 64.1%

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

   12. Simplified 64.1%

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

   if -1.14999999999999993e-33 < z < 3.39999999999999991e146

   1. Initial program 94.6%

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

   5. Taylor expanded in z around inf 61.1%

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

      1. associate-*l/ 63.1%

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

      2. *-commutative 63.1%

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

   7. Simplified 63.1%

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

      1. clear-num 63.1%

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

      2. un-div-inv 63.4%

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

   9. Applied egg-rr 63.4%

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

       1. div-inv 63.1%

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

       2. clear-num 63.1%

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

       3. cancel-sign-sub-inv 63.1%

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

       4. *-commutative 63.1%

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

       5. associate-/r/ 59.9%

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

       6. +-commutative 59.9%

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

       7. associate-/r/ 63.1%

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

       8. *-commutative 63.1%

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

       9. add-sqr-sqrt 24.0%

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

       10. sqrt-unprod 53.8%

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

       11. sqr-neg 53.8%

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

       12. sqrt-unprod 32.0%

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

       13. add-sqr-sqrt 53.4%

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

   11. Applied egg-rr 53.4%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-33} \lor \neg \left(z \leq 3.4 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+60} \lor \neg \left(z \leq 2.7 \cdot 10^{+141}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+60) (not (<= z 2.7e+141)))
   (- x (* (/ y a) z))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+60) || !(z <= 2.7e+141)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2d+60)) .or. (.not. (z <= 2.7d+141))) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + ((y / a) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+60) || !(z <= 2.7e+141)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+60) or not (z <= 2.7e+141):
		tmp = x - ((y / a) * z)
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+60) || !(z <= 2.7e+141))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+60) || ~((z <= 2.7e+141)))
		tmp = x - ((y / a) * z);
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+60], N[Not[LessEqual[z, 2.7e+141]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e60 or 2.7000000000000001e141 < z

   1. Initial program 83.4%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. associate-*l/ 94.4%

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

      2. *-commutative 94.4%

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

   7. Simplified 94.4%

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

   if -1.9999999999999999e60 < z < 2.7000000000000001e141

   1. Initial program 94.1%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l/ 86.7%

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

      3. neg-mul-1 86.7%

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

      4. distribute-rgt-neg-out 86.7%

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

   7. Simplified 86.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+60} \lor \neg \left(z \leq 2.7 \cdot 10^{+141}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-34} \lor \neg \left(z \leq 5.6 \cdot 10^{+147}\right):\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e-34) (not (<= z 5.6e+147))) (* y (/ (- z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e-34) || !(z <= 5.6e+147)) {
		tmp = y * (-z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6d-34)) .or. (.not. (z <= 5.6d+147))) then
        tmp = y * (-z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e-34) || !(z <= 5.6e+147)) {
		tmp = y * (-z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e-34) or not (z <= 5.6e+147):
		tmp = y * (-z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e-34) || !(z <= 5.6e+147))
		tmp = Float64(y * Float64(Float64(-z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6e-34) || ~((z <= 5.6e+147)))
		tmp = y * (-z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e-34], N[Not[LessEqual[z, 5.6e+147]], $MachinePrecision]], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6e-34 or 5.6000000000000002e147 < z

   1. Initial program 84.6%

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

   5. Taylor expanded in z around inf 75.6%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

   7. Simplified 85.2%

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

      1. clear-num 85.2%

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

      2. un-div-inv 85.2%

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

   9. Applied egg-rr 85.2%

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

   10. Taylor expanded in x around 0 55.2%

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

       1. mul-1-neg 55.2%

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

       2. associate-*r/ 59.4%

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

       3. distribute-rgt-neg-in 59.4%

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

   12. Simplified 59.4%

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

   if -6e-34 < z < 5.6000000000000002e147

   1. Initial program 94.6%

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

   5. Taylor expanded in z around inf 61.1%

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

      1. associate-*l/ 63.1%

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

      2. *-commutative 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in x around inf 50.9%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-34} \lor \neg \left(z \leq 5.6 \cdot 10^{+147}\right):\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-34} \lor \neg \left(z \leq 2.7 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-34) (not (<= z 2.7e+146))) (* (/ y a) (- z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-34) || !(z <= 2.7e+146)) {
		tmp = (y / a) * -z;
	} 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 ((z <= (-1.15d-34)) .or. (.not. (z <= 2.7d+146))) then
        tmp = (y / a) * -z
    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 ((z <= -1.15e-34) || !(z <= 2.7e+146)) {
		tmp = (y / a) * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-34) or not (z <= 2.7e+146):
		tmp = (y / a) * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-34) || !(z <= 2.7e+146))
		tmp = Float64(Float64(y / a) * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e-34) || ~((z <= 2.7e+146)))
		tmp = (y / a) * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-34], N[Not[LessEqual[z, 2.7e+146]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000006e-34 or 2.69999999999999989e146 < z

   1. Initial program 84.6%

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

   5. Taylor expanded in z around inf 75.6%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

   7. Simplified 85.2%

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

      1. clear-num 85.2%

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

      2. un-div-inv 85.2%

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

   9. Applied egg-rr 85.2%

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

   10. Taylor expanded in x around 0 55.2%

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

       1. *-commutative 55.2%

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

       2. associate-*r/ 64.1%

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

       3. associate-*r* 64.1%

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

       4. neg-mul-1 64.1%

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

   12. Simplified 64.1%

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

   if -1.15000000000000006e-34 < z < 2.69999999999999989e146

   1. Initial program 94.6%

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

   5. Taylor expanded in z around inf 61.1%

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

      1. associate-*l/ 63.1%

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

      2. *-commutative 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in x around inf 50.9%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-34} \lor \neg \left(z \leq 2.7 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around inf 67.0%

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

   1. associate-*l/ 72.1%

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

   2. *-commutative 72.1%

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

7. Simplified 72.1%

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

8. Final simplification 72.1%

   \[\leadsto x - \frac{y}{a} \cdot z \]
9. Add Preprocessing

Alternative 7: 71.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around inf 67.0%

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

   1. associate-*l/ 72.1%

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

   2. *-commutative 72.1%

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

7. Simplified 72.1%

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

   1. clear-num 72.0%

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

   2. un-div-inv 72.3%

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

9. Applied egg-rr 72.3%

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

10. Final simplification 72.3%

    \[\leadsto x - \frac{z}{\frac{a}{y}} \]
11. Add Preprocessing

Alternative 8: 39.6% 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 90.5%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around inf 67.0%

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

   1. associate-*l/ 72.1%

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

   2. *-commutative 72.1%

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

7. Simplified 72.1%

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

8. Taylor expanded in x around inf 39.5%

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

9. Final simplification 39.5%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 99.2% accurate, 0.5× 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 2024036 
(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)))