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

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

2. Final simplification 100.0%

   \[\leadsto \frac{\left(x + y\right) - z}{t \cdot 2} \]

Alternative 2: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-193}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 2400000:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e-193)
   (/ (* x 0.5) t)
   (if (<= y 2400000.0) (* (/ z t) -0.5) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-193) {
		tmp = (x * 0.5) / t;
	} else if (y <= 2400000.0) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (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 <= (-5.2d-193)) then
        tmp = (x * 0.5d0) / t
    else if (y <= 2400000.0d0) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = 0.5d0 * (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 <= -5.2e-193) {
		tmp = (x * 0.5) / t;
	} else if (y <= 2400000.0) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e-193:
		tmp = (x * 0.5) / t
	elif y <= 2400000.0:
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-193)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (y <= 2400000.0)
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e-193)
		tmp = (x * 0.5) / t;
	elseif (y <= 2400000.0)
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e-193], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 2400000.0], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.20000000000000015e-193

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in x around inf 31.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 31.6%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   4. Simplified 31.6%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -5.20000000000000015e-193 < y < 2.4e6

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in z around inf 57.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   4. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   if 2.4e6 < y

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around inf 67.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-193}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 2400000:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+96}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9e+96) (* 0.5 (/ (- x z) t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9e+96) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (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 <= 9d+96) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * (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 <= 9e+96) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9e+96:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9e+96)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 9e+96)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9e+96], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.99999999999999914e96

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around 0 74.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if 8.99999999999999914e96 < y

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around inf 79.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+96}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-36}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e-36) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-36) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / 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 (x <= (-4.2d-36)) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-36) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e-36:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e-36)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.2e-36)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e-36], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999982e-36

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around 0 76.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if -4.19999999999999982e-36 < x

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in x around 0 80.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y - z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-36}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 5: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{\frac{t}{y - \left(z - x\right)}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ 0.5 (/ t (- y (- z x)))))

C

double code(double x, double y, double z, double t) {
	return 0.5 / (t / (y - (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 = 0.5d0 / (t / (y - (z - x)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.5 / (t / (y - (z - x)));
}

Python

def code(x, y, z, t):
	return 0.5 / (t / (y - (z - x)))

Julia

function code(x, y, z, t)
	return Float64(0.5 / Float64(t / Float64(y - Float64(z - x))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.5 / (t / (y - (z - x)));
end

Wolfram

code[x_, y_, z_, t_] := N[(0.5 / N[(t / N[(y - N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. clear-num 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

   2. inv-pow 99.6%

      \[\leadsto \color{blue}{{\left(\frac{t \cdot 2}{\left(x + y\right) - z}\right)}^{-1}} \]

   3. *-commutative 99.6%

      \[\leadsto {\left(\frac{\color{blue}{2 \cdot t}}{\left(x + y\right) - z}\right)}^{-1} \]

   4. *-un-lft-identity 99.6%

      \[\leadsto {\left(\frac{2 \cdot t}{\color{blue}{1 \cdot \left(\left(x + y\right) - z\right)}}\right)}^{-1} \]

   5. times-frac 99.6%

      \[\leadsto {\color{blue}{\left(\frac{2}{1} \cdot \frac{t}{\left(x + y\right) - z}\right)}}^{-1} \]

   6. metadata-eval 99.6%

      \[\leadsto {\left(\color{blue}{2} \cdot \frac{t}{\left(x + y\right) - z}\right)}^{-1} \]

   7. associate--l+ 99.6%

      \[\leadsto {\left(2 \cdot \frac{t}{\color{blue}{x + \left(y - z\right)}}\right)}^{-1} \]

3. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{{\left(2 \cdot \frac{t}{x + \left(y - z\right)}\right)}^{-1}} \]
4. Step-by-step derivation

   1. unpow-1 99.6%

      \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{t}{x + \left(y - z\right)}}} \]

   2. associate-/r* 99.6%

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{t}{x + \left(y - z\right)}}} \]

   3. metadata-eval 99.6%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{t}{x + \left(y - z\right)}} \]

   4. +-commutative 99.6%

      \[\leadsto \frac{0.5}{\frac{t}{\color{blue}{\left(y - z\right) + x}}} \]

   5. associate-+l- 99.6%

      \[\leadsto \frac{0.5}{\frac{t}{\color{blue}{y - \left(z - x\right)}}} \]

5. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{y - \left(z - x\right)}}} \]

6. Final simplification 99.6%

   \[\leadsto \frac{0.5}{\frac{t}{y - \left(z - x\right)}} \]

Alternative 6: 47.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 225000:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 225000.0) (* (/ z t) -0.5) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 225000.0) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (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 <= 225000.0d0) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = 0.5d0 * (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 <= 225000.0) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 225000.0:
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 225000.0)
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 225000.0)
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 225000.0], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 225000

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in z around inf 45.8%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   4. Simplified 45.8%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   if 225000 < y

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around inf 67.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 225000:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 37.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \frac{y}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 0.5 (/ y t)))

C

double code(double x, double y, double z, double t) {
	return 0.5 * (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 = 0.5d0 * (y / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.5 * (y / t);
}

Python

def code(x, y, z, t):
	return 0.5 * (y / t)

Julia

function code(x, y, z, t)
	return Float64(0.5 * Float64(y / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.5 * (y / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

2. Taylor expanded in y around inf 38.2%

   \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]

3. Final simplification 38.2%

   \[\leadsto 0.5 \cdot \frac{y}{t} \]

Alternative 8: 3.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 0.0)

C

double code(double x, double y, double z, double t) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0;
}

Python

def code(x, y, z, t):
	return 0.0

Julia

function code(x, y, z, t)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_] := 0.0

Derivation

1. Initial program 100.0%

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

   1. clear-num 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

   2. inv-pow 99.6%

      \[\leadsto \color{blue}{{\left(\frac{t \cdot 2}{\left(x + y\right) - z}\right)}^{-1}} \]

   3. *-commutative 99.6%

      \[\leadsto {\left(\frac{\color{blue}{2 \cdot t}}{\left(x + y\right) - z}\right)}^{-1} \]

   4. *-un-lft-identity 99.6%

      \[\leadsto {\left(\frac{2 \cdot t}{\color{blue}{1 \cdot \left(\left(x + y\right) - z\right)}}\right)}^{-1} \]

   5. times-frac 99.6%

      \[\leadsto {\color{blue}{\left(\frac{2}{1} \cdot \frac{t}{\left(x + y\right) - z}\right)}}^{-1} \]

   6. metadata-eval 99.6%

      \[\leadsto {\left(\color{blue}{2} \cdot \frac{t}{\left(x + y\right) - z}\right)}^{-1} \]

   7. associate--l+ 99.6%

      \[\leadsto {\left(2 \cdot \frac{t}{\color{blue}{x + \left(y - z\right)}}\right)}^{-1} \]

3. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{{\left(2 \cdot \frac{t}{x + \left(y - z\right)}\right)}^{-1}} \]
4. Step-by-step derivation

   1. unpow-1 99.6%

      \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{t}{x + \left(y - z\right)}}} \]

   2. associate-*r/ 99.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{2 \cdot t}{x + \left(y - z\right)}}} \]

   3. count-2 99.6%

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

   4. associate-/r/ 99.7%

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

   5. flip-+ 0.0%

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

   6. +-inverses 0.0%

      \[\leadsto \frac{1}{\frac{\color{blue}{0}}{t - t}} \cdot \left(x + \left(y - z\right)\right) \]

   7. +-inverses 0.0%

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

   8. +-inverses 0.0%

      \[\leadsto \frac{1}{\frac{t - t}{\color{blue}{0}}} \cdot \left(x + \left(y - z\right)\right) \]

   9. +-inverses 0.0%

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

   10. clear-num 0.0%

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

   11. +-inverses 0.0%

       \[\leadsto \frac{\color{blue}{0}}{t - t} \cdot \left(x + \left(y - z\right)\right) \]

   12. +-inverses 0.0%

       \[\leadsto \frac{0}{\color{blue}{0}} \cdot \left(x + \left(y - z\right)\right) \]

   13. +-commutative 0.0%

       \[\leadsto \frac{0}{0} \cdot \color{blue}{\left(\left(y - z\right) + x\right)} \]

   14. associate-+l- 0.0%

       \[\leadsto \frac{0}{0} \cdot \color{blue}{\left(y - \left(z - x\right)\right)} \]

5. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\frac{0}{0} \cdot \left(y - \left(z - x\right)\right)} \]

7. Simplified 4.7%

   \[\leadsto \color{blue}{0} \]

8. Final simplification 4.7%

   \[\leadsto 0 \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))