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

Percentage Accurate: 93.0% → 97.4%

Time: 8.0s

Alternatives: 7

Speedup: 1.0×

• 24.7% 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: 97.4% 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 94.7%

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

5. Final simplification 98.1%

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

Alternative 2: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+97} \lor \neg \left(z \leq 6.6 \cdot 10^{-56}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.1e+97) (not (<= z 6.6e-56)))
   (+ x (* (/ y t) z))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.1e+97) || !(z <= 6.6e-56)) {
		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 <= (-6.1d+97)) .or. (.not. (z <= 6.6d-56))) 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 <= -6.1e+97) || !(z <= 6.6e-56)) {
		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 <= -6.1e+97) or not (z <= 6.6e-56):
		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 <= -6.1e+97) || !(z <= 6.6e-56))
		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 <= -6.1e+97) || ~((z <= 6.6e-56)))
		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, -6.1e+97], N[Not[LessEqual[z, 6.6e-56]], $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 < -6.1e97 or 6.59999999999999967e-56 < z

   1. Initial program 93.5%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 87.1%

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

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

   if -6.1e97 < z < 6.59999999999999967e-56

   1. Initial program 95.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

   7. Simplified 88.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+97} \lor \neg \left(z \leq 6.6 \cdot 10^{-56}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+97)
   (+ x (* (/ y t) z))
   (if (<= z 1.46e-55) (* x (- 1.0 (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+97) {
		tmp = x + ((y / t) * z);
	} else if (z <= 1.46e-55) {
		tmp = x * (1.0 - (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 <= (-1.05d+97)) then
        tmp = x + ((y / t) * z)
    else if (z <= 1.46d-55) then
        tmp = x * (1.0d0 - (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 <= -1.05e+97) {
		tmp = x + ((y / t) * z);
	} else if (z <= 1.46e-55) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+97:
		tmp = x + ((y / t) * z)
	elif z <= 1.46e-55:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+97)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif (z <= 1.46e-55)
		tmp = Float64(x * Float64(1.0 - 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 <= -1.05e+97)
		tmp = x + ((y / t) * z);
	elseif (z <= 1.46e-55)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+97], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e-55], N[(x * N[(1.0 - 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 < -1.05000000000000006e97

   1. Initial program 91.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 89.5%

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

      1. associate-*l/ 97.7%

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

      2. *-commutative 97.7%

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

   7. Simplified 97.7%

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

   if -1.05000000000000006e97 < z < 1.46000000000000009e-55

   1. Initial program 95.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

   7. Simplified 88.3%

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

   if 1.46000000000000009e-55 < z

   1. Initial program 94.5%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in z around inf 85.7%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

   7. Simplified 87.5%

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

      1. clear-num 87.5%

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

      2. div-inv 87.6%

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

   9. Applied egg-rr 87.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-7} \lor \neg \left(y \leq 1.32 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-7) (not (<= y 1.32e+110))) (* x (/ (- y) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-7) || !(y <= 1.32e+110)) {
		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 <= (-3.2d-7)) .or. (.not. (y <= 1.32d+110))) 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 <= -3.2e-7) || !(y <= 1.32e+110)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e-7) or not (y <= 1.32e+110):
		tmp = x * (-y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e-7) || !(y <= 1.32e+110))
		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 <= -3.2e-7) || ~((y <= 1.32e+110)))
		tmp = x * (-y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e-7], N[Not[LessEqual[y, 1.32e+110]], $MachinePrecision]], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e-7 or 1.32e110 < y

   1. Initial program 88.6%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in y around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-frac-neg 58.9%

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

   10. Simplified 58.9%

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

   if -3.2000000000000001e-7 < y < 1.32e110

   1. Initial program 98.1%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 58.2%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-7} \lor \neg \left(y \leq 1.32 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-7) (* y (/ (- x) t)) (if (<= y 1.25e+110) x (* x (/ (- y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-7) {
		tmp = y * (-x / t);
	} else if (y <= 1.25e+110) {
		tmp = x;
	} 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 <= (-5d-7)) then
        tmp = y * (-x / t)
    else if (y <= 1.25d+110) then
        tmp = x
    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 <= -5e-7) {
		tmp = y * (-x / t);
	} else if (y <= 1.25e+110) {
		tmp = x;
	} else {
		tmp = x * (-y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e-7:
		tmp = y * (-x / t)
	elif y <= 1.25e+110:
		tmp = x
	else:
		tmp = x * (-y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-7)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (y <= 1.25e+110)
		tmp = x;
	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 <= -5e-7)
		tmp = y * (-x / t);
	elseif (y <= 1.25e+110)
		tmp = x;
	else
		tmp = x * (-y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e-7], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+110], x, N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999977e-7

   1. Initial program 91.9%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in y around inf 58.6%

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

      1. associate-*r/ 58.6%

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

      2. *-commutative 58.6%

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

      3. neg-mul-1 58.6%

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

      4. distribute-rgt-neg-in 58.6%

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

      5. associate-*r/ 60.2%

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

   10. Simplified 60.2%

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

   if -4.99999999999999977e-7 < y < 1.24999999999999995e110

   1. Initial program 98.1%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 58.2%

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

   if 1.24999999999999995e110 < y

   1. Initial program 82.7%

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

   5. Taylor expanded in x around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in y around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. distribute-frac-neg 62.2%

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

   10. Simplified 62.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% 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 94.7%

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

5. Taylor expanded in x around inf 68.7%

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

   1. mul-1-neg 68.7%

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

   2. unsub-neg 68.7%

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

7. Simplified 68.7%

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

8. Final simplification 68.7%

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

Alternative 7: 38.4% 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 94.7%

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

5. Taylor expanded in y around 0 41.0%

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

6. Final simplification 41.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 90.8% 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 2024026 
(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)))