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

Percentage Accurate: 93.0% → 97.8%

Time: 6.0s

Alternatives: 5

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. associate-*l/ 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

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

Alternative 2: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+127} \lor \neg \left(x \leq 3.1 \cdot 10^{+20}\right):\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e+127) (not (<= x 3.1e+20)))
   (- x (* x (/ y t)))
   (+ x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e+127) || !(x <= 3.1e+20)) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4d+127)) .or. (.not. (x <= 3.1d+20))) then
        tmp = x - (x * (y / t))
    else
        tmp = x + (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e+127) || !(x <= 3.1e+20)) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e+127) or not (x <= 3.1e+20):
		tmp = x - (x * (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e+127) || !(x <= 3.1e+20))
		tmp = Float64(x - Float64(x * Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4e+127) || ~((x <= 3.1e+20)))
		tmp = x - (x * (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e+127], N[Not[LessEqual[x, 3.1e+20]], $MachinePrecision]], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999982e127 or 3.1e20 < x

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. distribute-rgt-in 93.6%

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

      3. *-lft-identity 93.6%

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

      4. mul-1-neg 93.6%

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

      5. distribute-lft-neg-in 93.6%

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

      6. associate-*l/ 85.7%

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

      7. unsub-neg 85.7%

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

      8. *-commutative 85.7%

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

      9. associate-*r/ 93.6%

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

   6. Simplified 93.6%

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

   if -3.99999999999999982e127 < x < 3.1e20

   1. Initial program 93.2%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 84.4%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   6. Simplified 88.1%

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

      1. clear-num 88.0%

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

      2. div-inv 88.1%

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

   8. Applied egg-rr 88.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+127} \lor \neg \left(x \leq 3.1 \cdot 10^{+20}\right):\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 3: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+128} \lor \neg \left(y \leq 10^{+89}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.4e+128) (not (<= y 1e+89))) (* x (/ (- y) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.4e+128) || !(y <= 1e+89)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.4d+128)) .or. (.not. (y <= 1d+89))) then
        tmp = x * (-y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.4e+128) || !(y <= 1e+89)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.4e+128) or not (y <= 1e+89):
		tmp = x * (-y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.4e+128) || !(y <= 1e+89))
		tmp = Float64(x * Float64(Float64(-y) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.4e+128) || ~((y <= 1e+89)))
		tmp = x * (-y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.4e+128], N[Not[LessEqual[y, 1e+89]], $MachinePrecision]], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000002e128 or 9.99999999999999995e88 < y

   1. Initial program 82.1%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. distribute-rgt-in 60.5%

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

      3. *-lft-identity 60.5%

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

      4. mul-1-neg 60.5%

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

      5. distribute-lft-neg-in 60.5%

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

      6. associate-*l/ 47.9%

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

      7. unsub-neg 47.9%

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

      8. *-commutative 47.9%

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

      9. associate-*r/ 60.5%

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

   6. Simplified 60.5%

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

      1. clear-num 60.5%

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

      2. div-inv 60.5%

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

   8. Applied egg-rr 60.5%

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

   9. Taylor expanded in t around 0 44.0%

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

       1. mul-1-neg 44.0%

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

       2. associate-*l/ 55.5%

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

       3. *-commutative 55.5%

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

       4. distribute-rgt-neg-in 55.5%

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

       5. distribute-neg-frac 55.5%

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

       6. neg-mul-1 55.5%

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

       7. associate-/l* 55.5%

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

       8. metadata-eval 55.5%

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

       9. associate-/r* 55.5%

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

       10. neg-mul-1 55.5%

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

       11. associate-*r/ 55.5%

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

       12. *-rgt-identity 55.5%

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

       13. distribute-neg-frac 55.5%

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

       14. associate-/r/ 51.4%

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

       15. *-commutative 51.4%

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

   11. Simplified 51.4%

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

   12. Taylor expanded in y around 0 44.0%

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

       1. mul-1-neg 44.0%

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

       2. associate-/l* 51.4%

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

       3. associate-/r/ 55.5%

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

       4. *-commutative 55.5%

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

       5. distribute-rgt-neg-in 55.5%

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

       6. distribute-neg-frac 55.5%

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

   14. Simplified 55.5%

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

   if -5.40000000000000002e128 < y < 9.99999999999999995e88

   1. Initial program 98.4%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 54.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+128} \lor \neg \left(y \leq 10^{+89}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6e+170) (+ x (* (/ y t) z)) (* x (/ (- y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e+170) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (-y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 6d+170) then
        tmp = x + ((y / t) * z)
    else
        tmp = x * (-y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e+170) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (-y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6e+170:
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (-y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6e+170)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(Float64(-y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6e+170)
		tmp = x + ((y / t) * z);
	else
		tmp = x * (-y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6e+170], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.99999999999999994e170

   1. Initial program 93.8%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. associate-*l/ 81.6%

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

      2. *-commutative 81.6%

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

   6. Simplified 81.6%

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

   if 5.99999999999999994e170 < y

   1. Initial program 84.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. distribute-rgt-in 73.3%

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

      3. *-lft-identity 73.3%

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

      4. mul-1-neg 73.3%

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

      5. distribute-lft-neg-in 73.3%

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

      6. associate-*l/ 61.1%

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

      7. unsub-neg 61.1%

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

      8. *-commutative 61.1%

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

      9. associate-*r/ 73.3%

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

   6. Simplified 73.3%

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

      1. clear-num 73.2%

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

      2. div-inv 73.3%

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

   8. Applied egg-rr 73.3%

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

   9. Taylor expanded in t around 0 61.3%

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

       1. mul-1-neg 61.3%

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

       2. associate-*l/ 73.5%

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

       3. *-commutative 73.5%

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

       4. distribute-rgt-neg-in 73.5%

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

       5. distribute-neg-frac 73.5%

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

       6. neg-mul-1 73.5%

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

       7. associate-/l* 73.4%

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

       8. metadata-eval 73.4%

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

       9. associate-/r* 73.4%

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

       10. neg-mul-1 73.4%

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

       11. associate-*r/ 73.5%

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

       12. *-rgt-identity 73.5%

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

       13. distribute-neg-frac 73.5%

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

       14. associate-/r/ 67.7%

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

       15. *-commutative 67.7%

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

   11. Simplified 67.7%

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

   12. Taylor expanded in y around 0 61.3%

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

       1. mul-1-neg 61.3%

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

       2. associate-/l* 67.6%

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

       3. associate-/r/ 73.5%

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

       4. *-commutative 73.5%

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

       5. distribute-rgt-neg-in 73.5%

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

       6. distribute-neg-frac 73.5%

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

   14. Simplified 73.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \end{array} \]

Alternative 5: 38.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 92.7%

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

   1. associate-*l/ 97.6%

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

3. Simplified 97.6%

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

4. Taylor expanded in y around 0 38.2%

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

5. Final simplification 38.2%

   \[\leadsto x \]

Developer target: 90.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))