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

Percentage Accurate: 92.9% → 97.7%

Time: 8.9s

Alternatives: 8

Speedup: 1.0×

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

Specification

Math

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

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: 92.9% 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: 97.7% 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 92.0%

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

5. Final simplification 98.0%

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

Alternative 2: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-58} \lor \neg \left(z \leq 0.0006\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e-58) (not (<= z 0.0006)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e-58) || !(z <= 0.0006)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (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 <= (-1.9d-58)) .or. (.not. (z <= 0.0006d0))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (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 <= -1.9e-58) || !(z <= 0.0006)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e-58) or not (z <= 0.0006):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e-58) || !(z <= 0.0006))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.9e-58) || ~((z <= 0.0006)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e-58], N[Not[LessEqual[z, 0.0006]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e-58 or 5.99999999999999947e-4 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.1%

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

      3. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*l/ 83.3%

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

      3. *-commutative 83.3%

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

   9. Simplified 83.3%

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

   if -1.8999999999999999e-58 < z < 5.99999999999999947e-4

   1. Initial program 92.0%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

   7. Simplified 89.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-58} \lor \neg \left(z \leq 0.0006\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-58} \lor \neg \left(z \leq 0.00055\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.32e-58) (not (<= z 0.00055)))
   (+ x (* (/ y t) z))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.32e-58) || !(z <= 0.00055)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (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 <= (-1.32d-58)) .or. (.not. (z <= 0.00055d0))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x * (1.0d0 - (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 <= -1.32e-58) || !(z <= 0.00055)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.32e-58) or not (z <= 0.00055):
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.32e-58) || !(z <= 0.00055))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.32e-58) || ~((z <= 0.00055)))
		tmp = x + ((y / t) * z);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.32e-58], N[Not[LessEqual[z, 0.00055]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.31999999999999993e-58 or 5.50000000000000033e-4 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-*l/ 92.1%

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

      2. *-commutative 92.1%

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

   7. Simplified 92.1%

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

   if -1.31999999999999993e-58 < z < 5.50000000000000033e-4

   1. Initial program 92.0%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

   7. Simplified 89.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-58} \lor \neg \left(z \leq 0.00055\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.00075:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.15e-58)
   (+ x (/ z (/ t y)))
   (if (<= z 0.00075) (* x (- 1.0 (/ y t))) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.15e-58) {
		tmp = x + (z / (t / y));
	} else if (z <= 0.00075) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	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 <= (-2.15d-58)) then
        tmp = x + (z / (t / y))
    else if (z <= 0.00075d0) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.15e-58) {
		tmp = x + (z / (t / y));
	} else if (z <= 0.00075) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.15e-58:
		tmp = x + (z / (t / y))
	elif z <= 0.00075:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.15e-58)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 0.00075)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.15e-58)
		tmp = x + (z / (t / y));
	elseif (z <= 0.00075)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.15e-58], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00075], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e-58

   1. Initial program 94.9%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

   7. Simplified 91.2%

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

      1. clear-num 91.1%

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

      2. div-inv 91.3%

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

   9. Applied egg-rr 91.3%

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

   if -2.15e-58 < z < 7.5000000000000002e-4

   1. Initial program 92.0%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

   7. Simplified 89.1%

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

   if 7.5000000000000002e-4 < z

   1. Initial program 88.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.00075:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.00068:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e-59)
   (+ x (/ z (/ t y)))
   (if (<= z 0.00068) (- x (* x (/ y t))) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-59) {
		tmp = x + (z / (t / y));
	} else if (z <= 0.00068) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	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 <= (-1.3d-59)) then
        tmp = x + (z / (t / y))
    else if (z <= 0.00068d0) then
        tmp = x - (x * (y / t))
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-59) {
		tmp = x + (z / (t / y));
	} else if (z <= 0.00068) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e-59:
		tmp = x + (z / (t / y))
	elif z <= 0.00068:
		tmp = x - (x * (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e-59)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 0.00068)
		tmp = Float64(x - Float64(x * Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.3e-59)
		tmp = x + (z / (t / y));
	elseif (z <= 0.00068)
		tmp = x - (x * (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e-59], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00068], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.29999999999999999e-59

   1. Initial program 94.9%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

   7. Simplified 91.2%

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

      1. clear-num 91.1%

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

      2. div-inv 91.3%

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

   9. Applied egg-rr 91.3%

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

   if -1.29999999999999999e-59 < z < 6.8e-4

   1. Initial program 92.0%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. mul-1-neg 81.6%

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

      3. distribute-lft-neg-out 81.6%

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

      4. *-commutative 81.6%

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

      5. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

      1. frac-2neg 85.0%

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

      2. div-inv 85.0%

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

      3. distribute-neg-frac 85.0%

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

      4. add-sqr-sqrt 45.3%

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

      5. sqrt-unprod 49.7%

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

      6. sqr-neg 49.7%

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

      7. sqrt-unprod 17.2%

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

      8. add-sqr-sqrt 43.9%

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

      9. frac-2neg 43.9%

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

      10. clear-num 43.9%

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

      11. cancel-sign-sub-inv 43.9%

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

      12. clear-num 43.9%

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

      13. div-inv 43.9%

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

      14. associate-/r/ 45.6%

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

      15. *-commutative 45.6%

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

      16. add-sqr-sqrt 18.1%

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

      17. sqrt-unprod 50.4%

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

      18. sqr-neg 50.4%

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

      19. sqrt-unprod 46.1%

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

      20. add-sqr-sqrt 89.1%

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

   9. Applied egg-rr 89.1%

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

   if 6.8e-4 < z

   1. Initial program 88.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.00068:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+57} \lor \neg \left(y \leq 2100\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+57) (not (<= y 2100.0))) (* x (/ (- y) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+57) || !(y <= 2100.0)) {
		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 <= (-3.8d+57)) .or. (.not. (y <= 2100.0d0))) 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 <= -3.8e+57) || !(y <= 2100.0)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+57) or not (y <= 2100.0):
		tmp = x * (-y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+57) || !(y <= 2100.0))
		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 <= -3.8e+57) || ~((y <= 2100.0)))
		tmp = x * (-y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+57], N[Not[LessEqual[y, 2100.0]], $MachinePrecision]], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999999e57 or 2100 < y

   1. Initial program 84.3%

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

   5. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in y around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. associate-*r/ 46.6%

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

      3. distribute-rgt-neg-out 46.6%

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

      4. distribute-frac-neg 46.6%

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

   10. Simplified 46.6%

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

   if -3.7999999999999999e57 < y < 2100

   1. Initial program 98.8%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around 0 54.8%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+57} \lor \neg \left(y \leq 2100\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{y}{t}\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

5. Taylor expanded in x around inf 64.7%

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

   1. mul-1-neg 64.7%

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

   2. unsub-neg 64.7%

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

7. Simplified 64.7%

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

8. Final simplification 64.7%

   \[\leadsto x \cdot \left(1 - \frac{y}{t}\right) \]
9. Add Preprocessing

Alternative 8: 38.2% 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 92.0%

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

5. Taylor expanded in y around 0 36.9%

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

6. Final simplification 36.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 91.1% 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 2024031 
(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)))