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

Percentage Accurate: 99.9% → 99.9%

Time: 7.8s

Alternatives: 9

Speedup: 1.0×

• 25.6% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e+56)
   (* 0.5 (/ x t))
   (if (<= x 6.4e-286) (/ (* z -0.5) t) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e+56) {
		tmp = 0.5 * (x / t);
	} else if (x <= 6.4e-286) {
		tmp = (z * -0.5) / 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 (x <= (-4.2d+56)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= 6.4d-286) then
        tmp = (z * (-0.5d0)) / 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 (x <= -4.2e+56) {
		tmp = 0.5 * (x / t);
	} else if (x <= 6.4e-286) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e+56:
		tmp = 0.5 * (x / t)
	elif x <= 6.4e-286:
		tmp = (z * -0.5) / t
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e+56)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= 6.4e-286)
		tmp = Float64(Float64(z * -0.5) / 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 (x <= -4.2e+56)
		tmp = 0.5 * (x / t);
	elseif (x <= 6.4e-286)
		tmp = (z * -0.5) / t;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e+56], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e-286], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.20000000000000034e56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.7%

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

   if -4.20000000000000034e56 < x < 6.40000000000000014e-286

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 48.4%

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

      1. associate-*r/ 48.4%

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

   5. Simplified 48.4%

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

   if 6.40000000000000014e-286 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 39.1%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+57}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-285}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.1e+57)
   (* 0.5 (/ x t))
   (if (<= x 1.35e-285) (/ -0.5 (/ t z)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.1e+57) {
		tmp = 0.5 * (x / t);
	} else if (x <= 1.35e-285) {
		tmp = -0.5 / (t / z);
	} 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 (x <= (-6.1d+57)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= 1.35d-285) then
        tmp = (-0.5d0) / (t / z)
    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 (x <= -6.1e+57) {
		tmp = 0.5 * (x / t);
	} else if (x <= 1.35e-285) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.1e+57:
		tmp = 0.5 * (x / t)
	elif x <= 1.35e-285:
		tmp = -0.5 / (t / z)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.1e+57)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= 1.35e-285)
		tmp = Float64(-0.5 / Float64(t / z));
	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 (x <= -6.1e+57)
		tmp = 0.5 * (x / t);
	elseif (x <= 1.35e-285)
		tmp = -0.5 / (t / z);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.1e+57], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-285], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.09999999999999975e57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.7%

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

   if -6.09999999999999975e57 < x < 1.3499999999999999e-285

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 48.4%

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

      1. associate-*r/ 48.4%

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

   5. Simplified 48.4%

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

      1. clear-num 48.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{-0.5 \cdot z}}} \]

      2. inv-pow 48.2%

         \[\leadsto \color{blue}{{\left(\frac{t}{-0.5 \cdot z}\right)}^{-1}} \]

      3. *-un-lft-identity 48.2%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot t}}{-0.5 \cdot z}\right)}^{-1} \]

      4. times-frac 48.2%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.5} \cdot \frac{t}{z}\right)}}^{-1} \]

      5. metadata-eval 48.2%

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

   7. Applied egg-rr 48.2%

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

      1. unpow-1 48.2%

         \[\leadsto \color{blue}{\frac{1}{-2 \cdot \frac{t}{z}}} \]

      2. associate-/r* 48.2%

         \[\leadsto \color{blue}{\frac{\frac{1}{-2}}{\frac{t}{z}}} \]

      3. metadata-eval 48.2%

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

   9. Simplified 48.2%

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

   if 1.3499999999999999e-285 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 39.1%

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

Alternative 4: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e-16) (/ (- x z) (* t 2.0)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-16) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (0.5 / t) * (y - 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 (x <= (-8.5d-16)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (0.5d0 / t) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-16) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e-16:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e-16)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e-16)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e-16], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.1%

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]

   if -8.5000000000000001e-16 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 78.9%

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

      3. associate-*r/ 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e-16) (* (/ 0.5 t) (- x z)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-16) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (0.5 / t) * (y - 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 (x <= (-8.5d-16)) then
        tmp = (0.5d0 / t) * (x - z)
    else
        tmp = (0.5d0 / t) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-16) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e-16:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e-16)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e-16)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e-16], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 95.4%

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

      2. associate-*l/ 95.4%

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

      3. associate-*r/ 95.4%

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

      4. associate-*l/ 95.2%

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

      5. distribute-lft-in 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 84.9%

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

   if -8.5000000000000001e-16 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 78.9%

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

      3. associate-*r/ 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+57}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e+57) (* 0.5 (/ x t)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e+57) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (0.5 / t) * (y - 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 (x <= (-7.6d+57)) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = (0.5d0 / t) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e+57) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.6e+57:
		tmp = 0.5 * (x / t)
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e+57)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.6e+57)
		tmp = 0.5 * (x / t);
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e+57], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5999999999999997e57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.7%

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

   if -7.5999999999999997e57 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-*l/ 79.6%

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

      3. associate-*r/ 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+57}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12500000000000:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -12500000000000.0) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -12500000000000.0) {
		tmp = 0.5 * (x / 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 (x <= (-12500000000000.0d0)) then
        tmp = 0.5d0 * (x / 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 (x <= -12500000000000.0) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -12500000000000.0:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -12500000000000.0)
		tmp = Float64(0.5 * Float64(x / 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 (x <= -12500000000000.0)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -12500000000000.0], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.5%

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

   if -1.25e13 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 44.6%

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

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (x + (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 97.2%

   \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
4. Step-by-step derivation

   1. associate-*r/ 97.2%

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

   2. associate-*l/ 97.1%

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

   3. associate-*r/ 97.1%

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

   4. associate-*l/ 97.0%

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

   5. distribute-lft-in 99.7%

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

   6. +-commutative 99.7%

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

5. Simplified 99.7%

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

6. Final simplification 99.7%

   \[\leadsto \frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right) \]
7. Add Preprocessing

Alternative 9: 37.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 36.6%

   \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024135 
(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)))