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

Percentage Accurate: 92.6% → 97.6%

Time: 8.5s

Alternatives: 6

Speedup: 1.0×

• 24.9% 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: 92.6% 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: 97.6% 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 94.0%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-280} \lor \neg \left(z \leq 7.5 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e-280) (not (<= z 7.5e-142)))
   (+ x (* (/ y t) z))
   (* x (/ y (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e-280) || !(z <= 7.5e-142)) {
		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 ((z <= (-3.1d-280)) .or. (.not. (z <= 7.5d-142))) 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 ((z <= -3.1e-280) || !(z <= 7.5e-142)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e-280) or not (z <= 7.5e-142):
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (y / -t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e-280) || !(z <= 7.5e-142))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(y / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e-280) || ~((z <= 7.5e-142)))
		tmp = x + ((y / t) * z);
	else
		tmp = x * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e-280], N[Not[LessEqual[z, 7.5e-142]], $MachinePrecision]], 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 z < -3.10000000000000021e-280 or 7.49999999999999958e-142 < z

   1. Initial program 93.5%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. associate-*l/ 82.1%

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

      2. *-commutative 82.1%

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

   6. Simplified 82.1%

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

   if -3.10000000000000021e-280 < z < 7.49999999999999958e-142

   1. Initial program 96.0%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 97.9%

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

      1. distribute-lft-in 97.9%

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

      2. *-rgt-identity 97.9%

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

      3. mul-1-neg 97.9%

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

      4. distribute-rgt-neg-in 97.9%

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

      5. distribute-lft-neg-out 97.9%

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

      6. neg-mul-1 97.9%

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

      7. associate-*r* 97.9%

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

      8. associate-*r/ 94.2%

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

      9. mul-1-neg 94.2%

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

      10. unsub-neg 94.2%

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

      11. associate-*r/ 97.9%

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

   6. Simplified 97.9%

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

      1. clear-num 97.8%

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

      2. div-inv 97.9%

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

      3. clear-num 97.9%

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

   8. Applied egg-rr 97.9%

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

   9. Taylor expanded in t around 0 63.0%

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

       1. mul-1-neg 63.0%

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

       2. associate-*l/ 58.4%

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

       3. distribute-rgt-neg-in 58.4%

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

       4. *-commutative 58.4%

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

   11. Simplified 58.4%

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

   12. Taylor expanded in y around 0 63.0%

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

       1. associate-*r/ 63.0%

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

       2. *-commutative 63.0%

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

       3. associate-/l* 62.8%

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

       4. associate-/r/ 63.0%

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

       5. metadata-eval 63.0%

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

       6. associate-/r* 63.0%

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

       7. neg-mul-1 63.0%

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

       8. associate-*l/ 63.0%

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

       9. *-lft-identity 63.0%

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

       10. associate-/l* 58.4%

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

       11. associate-/r/ 65.2%

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

       12. *-commutative 65.2%

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

   14. Simplified 65.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-280} \lor \neg \left(z \leq 7.5 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+46}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+18)
   (+ x (* (/ y t) z))
   (if (<= z 2.2e+46) (- x (* x (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+18) {
		tmp = x + ((y / t) * z);
	} else if (z <= 2.2e+46) {
		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 (z <= (-1.1d+18)) then
        tmp = x + ((y / t) * z)
    else if (z <= 2.2d+46) 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 (z <= -1.1e+18) {
		tmp = x + ((y / t) * z);
	} else if (z <= 2.2e+46) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+18:
		tmp = x + ((y / t) * z)
	elif z <= 2.2e+46:
		tmp = x - (x * (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+18)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif (z <= 2.2e+46)
		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 (z <= -1.1e+18)
		tmp = x + ((y / t) * z);
	elseif (z <= 2.2e+46)
		tmp = x - (x * (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e+18], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+46], 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 3 regimes

2. if z < -1.1e18

   1. Initial program 85.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 78.2%

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

      1. associate-*l/ 89.9%

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

      2. *-commutative 89.9%

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

   6. Simplified 89.9%

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

   if -1.1e18 < z < 2.2e46

   1. Initial program 97.8%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.7%

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

      1. distribute-lft-in 86.7%

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

      2. *-rgt-identity 86.7%

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

      3. mul-1-neg 86.7%

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

      4. distribute-rgt-neg-in 86.7%

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

      5. distribute-lft-neg-out 86.7%

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

      6. neg-mul-1 86.7%

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

      7. associate-*r* 86.7%

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

      8. associate-*r/ 86.0%

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

      9. mul-1-neg 86.0%

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

      10. unsub-neg 86.0%

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

      11. associate-*r/ 86.7%

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

   6. Simplified 86.7%

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

   if 2.2e46 < z

   1. Initial program 95.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 z around inf 91.4%

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

      1. associate-*l/ 95.6%

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

      2. *-commutative 95.6%

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

   6. Simplified 95.6%

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

      1. clear-num 95.5%

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

      2. div-inv 95.6%

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

   8. Applied egg-rr 95.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+46}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 4: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+46}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e+18)
   (+ x (* (/ y t) z))
   (if (<= z 2.22e+46) (- x (/ x (/ t y))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+18) {
		tmp = x + ((y / t) * z);
	} else if (z <= 2.22e+46) {
		tmp = x - (x / (t / y));
	} 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 (z <= (-2.4d+18)) then
        tmp = x + ((y / t) * z)
    else if (z <= 2.22d+46) then
        tmp = x - (x / (t / y))
    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 (z <= -2.4e+18) {
		tmp = x + ((y / t) * z);
	} else if (z <= 2.22e+46) {
		tmp = x - (x / (t / y));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e+18:
		tmp = x + ((y / t) * z)
	elif z <= 2.22e+46:
		tmp = x - (x / (t / y))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e+18)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif (z <= 2.22e+46)
		tmp = Float64(x - Float64(x / Float64(t / y)));
	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 (z <= -2.4e+18)
		tmp = x + ((y / t) * z);
	elseif (z <= 2.22e+46)
		tmp = x - (x / (t / y));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e+18], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.22e+46], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e18

   1. Initial program 85.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 78.2%

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

      1. associate-*l/ 89.9%

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

      2. *-commutative 89.9%

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

   6. Simplified 89.9%

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

   if -2.4e18 < z < 2.21999999999999999e46

   1. Initial program 97.8%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.7%

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

      1. distribute-lft-in 86.7%

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

      2. *-rgt-identity 86.7%

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

      3. mul-1-neg 86.7%

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

      4. distribute-rgt-neg-in 86.7%

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

      5. distribute-lft-neg-out 86.7%

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

      6. neg-mul-1 86.7%

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

      7. associate-*r* 86.7%

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

      8. associate-*r/ 86.0%

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

      9. mul-1-neg 86.0%

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

      10. unsub-neg 86.0%

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

      11. associate-*r/ 86.7%

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

   6. Simplified 86.7%

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

      1. clear-num 86.7%

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

      2. div-inv 87.0%

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

   8. Applied egg-rr 87.0%

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

   if 2.21999999999999999e46 < z

   1. Initial program 95.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 z around inf 91.4%

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

      1. associate-*l/ 95.6%

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

      2. *-commutative 95.6%

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

   6. Simplified 95.6%

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

      1. clear-num 95.5%

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

      2. div-inv 95.6%

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

   8. Applied egg-rr 95.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+46}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 5: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -580000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -580000000000.0) x (if (<= t 1.45e+23) (* x (/ y (- t))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -580000000000.0) {
		tmp = x;
	} else if (t <= 1.45e+23) {
		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 (t <= (-580000000000.0d0)) then
        tmp = x
    else if (t <= 1.45d+23) 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 (t <= -580000000000.0) {
		tmp = x;
	} else if (t <= 1.45e+23) {
		tmp = x * (y / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -580000000000.0:
		tmp = x
	elif t <= 1.45e+23:
		tmp = x * (y / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -580000000000.0)
		tmp = x;
	elseif (t <= 1.45e+23)
		tmp = Float64(x * Float64(y / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -580000000000.0)
		tmp = x;
	elseif (t <= 1.45e+23)
		tmp = x * (y / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -580000000000.0], x, If[LessEqual[t, 1.45e+23], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8e11 or 1.45000000000000006e23 < t

   1. Initial program 87.7%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 y around 0 57.9%

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

   if -5.8e11 < t < 1.45000000000000006e23

   1. Initial program 99.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 59.5%

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

      1. distribute-lft-in 59.5%

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

      2. *-rgt-identity 59.5%

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

      3. mul-1-neg 59.5%

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

      4. distribute-rgt-neg-in 59.5%

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

      5. distribute-lft-neg-out 59.5%

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

      6. neg-mul-1 59.5%

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

      7. associate-*r* 59.5%

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

      8. associate-*r/ 58.8%

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

      9. mul-1-neg 58.8%

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

      10. unsub-neg 58.8%

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

      11. associate-*r/ 59.5%

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

   6. Simplified 59.5%

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

      1. clear-num 59.4%

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

      2. div-inv 59.8%

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

      3. clear-num 59.8%

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

   8. Applied egg-rr 59.8%

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

   9. Taylor expanded in t around 0 46.3%

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

       1. mul-1-neg 46.3%

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

       2. associate-*l/ 43.1%

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

       3. distribute-rgt-neg-in 43.1%

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

       4. *-commutative 43.1%

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

   11. Simplified 43.1%

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

   12. Taylor expanded in y around 0 46.3%

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

       1. associate-*r/ 46.3%

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

       2. *-commutative 46.3%

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

       3. associate-/l* 46.2%

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

       4. associate-/r/ 46.3%

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

       5. metadata-eval 46.3%

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

       6. associate-/r* 46.3%

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

       7. neg-mul-1 46.3%

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

       8. associate-*l/ 46.3%

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

       9. *-lft-identity 46.3%

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

       10. associate-/l* 43.1%

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

       11. associate-/r/ 47.0%

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

       12. *-commutative 47.0%

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

   14. Simplified 47.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -580000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 38.5% 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 94.0%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in y around 0 34.0%

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

5. Final simplification 34.0%

   \[\leadsto x \]

Developer target: 91.0% 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 2023279 
(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)))