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

Percentage Accurate: 92.9% → 97.9%

Time: 8.3s

Alternatives: 8

Speedup: 1.0×

• 24.6% 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: 97.9% 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 92.1%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
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. Final simplification 98.4%

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

Alternative 2: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-75} \lor \neg \left(t \leq 8.5 \cdot 10^{-73}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e-75) (not (<= t 8.5e-73)))
   (+ x (* (/ y t) z))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e-75) || !(t <= 8.5e-73)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = (y / t) * (z - 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 <= (-8d-75)) .or. (.not. (t <= 8.5d-73))) then
        tmp = x + ((y / t) * z)
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e-75) || !(t <= 8.5e-73)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e-75) or not (t <= 8.5e-73):
		tmp = x + ((y / t) * z)
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8e-75) || !(t <= 8.5e-73))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8e-75) || ~((t <= 8.5e-73)))
		tmp = x + ((y / t) * z);
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8e-75], N[Not[LessEqual[t, 8.5e-73]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.9999999999999997e-75 or 8.4999999999999996e-73 < t

   1. Initial program 88.7%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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. Taylor expanded in z around inf 85.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   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 -7.9999999999999997e-75 < t < 8.4999999999999996e-73

   1. Initial program 98.2%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-*l/ 98.2%

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

      3. clear-num 98.2%

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

      4. associate-/r/ 98.3%

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

      5. fma-def 98.3%

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

   5. Applied egg-rr 98.3%

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

   6. Taylor expanded in t around 0 92.4%

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

      1. associate-/l* 82.5%

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

   8. Simplified 82.5%

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

      1. associate-/r/ 90.5%

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

   10. Applied egg-rr 90.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-75} \lor \neg \left(t \leq 8.5 \cdot 10^{-73}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]

Alternative 3: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-75} \lor \neg \left(t \leq 7.5 \cdot 10^{+41}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-75) (not (<= t 7.5e+41)))
   (+ x (* (/ y t) z))
   (/ (* y (- z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-75) || !(t <= 7.5e+41)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = (y * (z - x)) / 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 ((t <= (-8.5d-75)) .or. (.not. (t <= 7.5d+41))) then
        tmp = x + ((y / t) * z)
    else
        tmp = (y * (z - x)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-75) || !(t <= 7.5e+41)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = (y * (z - x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e-75) or not (t <= 7.5e+41):
		tmp = x + ((y / t) * z)
	else:
		tmp = (y * (z - x)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e-75) || !(t <= 7.5e+41))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e-75) || ~((t <= 7.5e+41)))
		tmp = x + ((y / t) * z);
	else
		tmp = (y * (z - x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e-75], N[Not[LessEqual[t, 7.5e+41]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000001e-75 or 7.50000000000000072e41 < t

   1. Initial program 87.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.1%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

   6. Simplified 93.1%

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

   if -8.5000000000000001e-75 < t < 7.50000000000000072e41

   1. Initial program 98.5%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-*l/ 98.5%

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

      3. clear-num 98.4%

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

      4. associate-/r/ 98.6%

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

      5. fma-def 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in t around 0 87.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-75} \lor \neg \left(t \leq 7.5 \cdot 10^{+41}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]

Alternative 4: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.05e+55) x (if (<= t 3.3e+182) (* (/ y t) (- z x)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e+55) {
		tmp = x;
	} else if (t <= 3.3e+182) {
		tmp = (y / t) * (z - x);
	} 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 <= (-2.05d+55)) then
        tmp = x
    else if (t <= 3.3d+182) then
        tmp = (y / t) * (z - x)
    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 <= -2.05e+55) {
		tmp = x;
	} else if (t <= 3.3e+182) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.05e+55:
		tmp = x
	elif t <= 3.3e+182:
		tmp = (y / t) * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.05e+55)
		tmp = x;
	elseif (t <= 3.3e+182)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.05e+55)
		tmp = x;
	elseif (t <= 3.3e+182)
		tmp = (y / t) * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.05e+55], x, If[LessEqual[t, 3.3e+182], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.04999999999999991e55 or 3.3000000000000001e182 < t

   1. Initial program 83.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 78.3%

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

   if -2.04999999999999991e55 < t < 3.3000000000000001e182

   1. Initial program 97.7%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-*l/ 97.7%

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

      3. clear-num 97.6%

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

      4. associate-/r/ 97.7%

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

      5. fma-def 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in t around 0 80.3%

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

      1. associate-/l* 75.5%

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

   8. Simplified 75.5%

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

      1. associate-/r/ 79.7%

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

   10. Applied egg-rr 79.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.2e-75)
   (+ x (* (/ y t) z))
   (if (<= t 1.32e-69) (* (/ y t) (- z x)) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-75) {
		tmp = x + ((y / t) * z);
	} else if (t <= 1.32e-69) {
		tmp = (y / t) * (z - x);
	} 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 (t <= (-8.2d-75)) then
        tmp = x + ((y / t) * z)
    else if (t <= 1.32d-69) then
        tmp = (y / t) * (z - x)
    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 (t <= -8.2e-75) {
		tmp = x + ((y / t) * z);
	} else if (t <= 1.32e-69) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.2e-75:
		tmp = x + ((y / t) * z)
	elif t <= 1.32e-69:
		tmp = (y / t) * (z - x)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.2e-75)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif (t <= 1.32e-69)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.2e-75)
		tmp = x + ((y / t) * z);
	elseif (t <= 1.32e-69)
		tmp = (y / t) * (z - x);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.2e-75], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e-69], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.20000000000000005e-75

   1. Initial program 87.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 89.2%

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

      1. associate-*l/ 94.0%

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

      2. *-commutative 94.0%

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

   6. Simplified 94.0%

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

   if -8.20000000000000005e-75 < t < 1.32000000000000007e-69

   1. Initial program 98.2%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-*l/ 98.2%

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

      3. clear-num 98.2%

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

      4. associate-/r/ 98.3%

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

      5. fma-def 98.3%

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

   5. Applied egg-rr 98.3%

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

   6. Taylor expanded in t around 0 92.4%

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

      1. associate-/l* 82.5%

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

   8. Simplified 82.5%

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

      1. associate-/r/ 90.5%

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

   10. Applied egg-rr 90.5%

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

   if 1.32000000000000007e-69 < t

   1. Initial program 89.8%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 86.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e+50) x (if (<= t 9.8e+185) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e+50) {
		tmp = x;
	} else if (t <= 9.8e+185) {
		tmp = y * (z / 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 <= (-1.4d+50)) then
        tmp = x
    else if (t <= 9.8d+185) then
        tmp = y * (z / 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 <= -1.4e+50) {
		tmp = x;
	} else if (t <= 9.8e+185) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e+50:
		tmp = x
	elif t <= 9.8e+185:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e+50)
		tmp = x;
	elseif (t <= 9.8e+185)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e+50)
		tmp = x;
	elseif (t <= 9.8e+185)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e+50], x, If[LessEqual[t, 9.8e+185], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e50 or 9.79999999999999968e185 < t

   1. Initial program 83.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 78.3%

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

   if -1.3999999999999999e50 < t < 9.79999999999999968e185

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-*r/ 92.1%

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

      3. fma-def 92.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. add-cube-cbrt 91.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{y \cdot \frac{z - x}{t} + x} \cdot \sqrt[3]{y \cdot \frac{z - x}{t} + x}\right) \cdot \sqrt[3]{y \cdot \frac{z - x}{t} + x}} \]

      2. pow3 91.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \frac{z - x}{t} + x}\right)}^{3}} \]

      3. fma-def 91.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)}}\right)}^{3} \]

   7. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)}\right)}^{3}} \]

   8. Taylor expanded in x around 0 47.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. pow-base-1 47.5%

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

      2. associate-*r/ 45.3%

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

      3. *-lft-identity 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.7e+47) x (if (<= t 3.1e+182) (* (/ y t) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e+47) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		tmp = (y / t) * z;
	} 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 <= (-2.7d+47)) then
        tmp = x
    else if (t <= 3.1d+182) then
        tmp = (y / t) * z
    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 <= -2.7e+47) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.7e+47:
		tmp = x
	elif t <= 3.1e+182:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.7e+47)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.7e+47)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.7e+47], x, If[LessEqual[t, 3.1e+182], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999996e47 or 3.09999999999999996e182 < t

   1. Initial program 83.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 78.3%

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

   if -2.69999999999999996e47 < t < 3.09999999999999996e182

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-*r/ 92.1%

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

      3. fma-def 92.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. add-cube-cbrt 91.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{y \cdot \frac{z - x}{t} + x} \cdot \sqrt[3]{y \cdot \frac{z - x}{t} + x}\right) \cdot \sqrt[3]{y \cdot \frac{z - x}{t} + x}} \]

      2. pow3 91.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \frac{z - x}{t} + x}\right)}^{3}} \]

      3. fma-def 91.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)}}\right)}^{3} \]

   7. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)}\right)}^{3}} \]

   8. Taylor expanded in x around 0 47.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. pow-base-1 47.5%

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

      2. associate-*r/ 47.5%

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

      3. *-lft-identity 47.5%

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

      4. associate-*l/ 51.1%

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

      5. *-commutative 51.1%

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

   10. Simplified 51.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 39.0% 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 92.1%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
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. Taylor expanded in y around 0 41.7%

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

5. Final simplification 41.7%

   \[\leadsto x \]

Developer target: 90.9% 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 2023199 
(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)))