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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 9

Speedup: 1.0×

• 22.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 - z) * (x + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Final simplification 100.0%

   \[\leadsto \left(1 - z\right) \cdot \left(x + y\right) \]

Alternative 2: 75.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -1000000000000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 1.01:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 z) -2e+114)
   (* y (- z))
   (if (<= (- 1.0 z) -1000000000000.0)
     (* z (- x))
     (if (<= (- 1.0 z) 1.01) (+ x y) (* y (- 1.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - z) <= -2e+114) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -1000000000000.0) {
		tmp = z * -x;
	} else if ((1.0 - z) <= 1.01) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((1.0d0 - z) <= (-2d+114)) then
        tmp = y * -z
    else if ((1.0d0 - z) <= (-1000000000000.0d0)) then
        tmp = z * -x
    else if ((1.0d0 - z) <= 1.01d0) then
        tmp = x + y
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - z) <= -2e+114) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -1000000000000.0) {
		tmp = z * -x;
	} else if ((1.0 - z) <= 1.01) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - z) <= -2e+114:
		tmp = y * -z
	elif (1.0 - z) <= -1000000000000.0:
		tmp = z * -x
	elif (1.0 - z) <= 1.01:
		tmp = x + y
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - z) <= -2e+114)
		tmp = Float64(y * Float64(-z));
	elseif (Float64(1.0 - z) <= -1000000000000.0)
		tmp = Float64(z * Float64(-x));
	elseif (Float64(1.0 - z) <= 1.01)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - z) <= -2e+114)
		tmp = y * -z;
	elseif ((1.0 - z) <= -1000000000000.0)
		tmp = z * -x;
	elseif ((1.0 - z) <= 1.01)
		tmp = x + y;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - z), $MachinePrecision], -2e+114], N[(y * (-z)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], -1000000000000.0], N[(z * (-x)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.01], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 z) < -2e114

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 41.6%

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

      1. associate-*r* 41.6%

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

      2. mul-1-neg 41.6%

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

   7. Simplified 41.6%

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

   if -2e114 < (-.f64 1 z) < -1e12

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 49.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 49.3%

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

   4. Simplified 49.3%

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

   5. Taylor expanded in z around inf 49.3%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 49.3%

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

   if -1e12 < (-.f64 1 z) < 1.01000000000000001

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.5%

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

      1. +-commutative 98.5%

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

   4. Simplified 98.5%

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

   if 1.01000000000000001 < (-.f64 1 z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around 0 58.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -1000000000000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 1.01:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -1000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -1000000000000.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- y) x))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -1000000000000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - z) <= (-1000000000000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-y - x)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -1000000000000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -1000000000000.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-y - x)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -1000000000000.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-y) - x));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -1000000000000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-y - x);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -1000000000000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -1e12 or 2 < (-.f64 1 z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. *-commutative 99.1%

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

      3. distribute-rgt-neg-out 99.1%

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

      4. +-commutative 99.1%

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

   4. Simplified 99.1%

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

   if -1e12 < (-.f64 1 z) < 2

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.0%

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

      1. +-commutative 98.0%

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

   4. Simplified 98.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -1000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq 3.4 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 z))))
   (if (<= y 3.4e-77)
     t_0
     (if (<= y 6e+26) (+ x y) (if (<= y 3.2e+43) t_0 (* y (- 1.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (y <= 3.4e-77) {
		tmp = t_0;
	} else if (y <= 6e+26) {
		tmp = x + y;
	} else if (y <= 3.2e+43) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - z)
    if (y <= 3.4d-77) then
        tmp = t_0
    else if (y <= 6d+26) then
        tmp = x + y
    else if (y <= 3.2d+43) then
        tmp = t_0
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (y <= 3.4e-77) {
		tmp = t_0;
	} else if (y <= 6e+26) {
		tmp = x + y;
	} else if (y <= 3.2e+43) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - z)
	tmp = 0
	if y <= 3.4e-77:
		tmp = t_0
	elif y <= 6e+26:
		tmp = x + y
	elif y <= 3.2e+43:
		tmp = t_0
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (y <= 3.4e-77)
		tmp = t_0;
	elseif (y <= 6e+26)
		tmp = Float64(x + y);
	elseif (y <= 3.2e+43)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - z);
	tmp = 0.0;
	if (y <= 3.4e-77)
		tmp = t_0;
	elseif (y <= 6e+26)
		tmp = x + y;
	elseif (y <= 3.2e+43)
		tmp = t_0;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 3.4e-77], t$95$0, If[LessEqual[y, 6e+26], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.2e+43], t$95$0, N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.39999999999999983e-77 or 5.99999999999999994e26 < y < 3.20000000000000014e43

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 59.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   if 3.39999999999999983e-77 < y < 5.99999999999999994e26

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 72.0%

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

      1. +-commutative 72.0%

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

   4. Simplified 72.0%

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

   if 3.20000000000000014e43 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around 0 78.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -26.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= z -26.5)
     t_0
     (if (<= z 1.0) (+ x y) (if (<= z 1.65e+113) (* z (- x)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -26.5) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if (z <= 1.65e+113) {
		tmp = z * -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -z
    if (z <= (-26.5d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if (z <= 1.65d+113) then
        tmp = z * -x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -26.5) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if (z <= 1.65e+113) {
		tmp = z * -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if z <= -26.5:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif z <= 1.65e+113:
		tmp = z * -x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -26.5)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif (z <= 1.65e+113)
		tmp = Float64(z * Float64(-x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (z <= -26.5)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif (z <= 1.65e+113)
		tmp = z * -x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -26.5], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.65e+113], N[(z * (-x)), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -26.5 or 1.6500000000000002e113 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. *-commutative 99.2%

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

      3. distribute-rgt-neg-out 99.2%

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

      4. +-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 50.8%

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

      1. associate-*r* 50.8%

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

      2. mul-1-neg 50.8%

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

   7. Simplified 50.8%

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

   if -26.5 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.0%

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

      1. +-commutative 98.0%

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

   4. Simplified 98.0%

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

   if 1 < z < 1.6500000000000002e113

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 49.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 49.3%

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

   4. Simplified 49.3%

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

   5. Taylor expanded in z around inf 49.3%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 49.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26.5:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -105.0) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -105.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-105.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -105.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -105.0) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -105.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -105.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -105.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -105 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 54.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in z around inf 54.9%

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

      1. associate-*r* 99.2%

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

      2. mul-1-neg 99.2%

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

   7. Simplified 54.9%

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

   if -105 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 97.4%

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

      1. +-commutative 97.4%

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

   4. Simplified 97.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 32.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 4.6e-53) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e-53) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 4.6d-53) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e-53) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.6e-53:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.6e-53)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.6e-53)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.6e-53], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 4.6000000000000003e-53

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 59.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in z around 0 29.8%

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

   if 4.6000000000000003e-53 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 97.3%

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

      4. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 83.9%

      \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{-1 \cdot \left(x \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 83.9%

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

      2. mul-1-neg 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in z around 0 36.9%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 51.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x y))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + y
end function

Java

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

Python

def code(x, y, z):
	return x + y

Julia

function code(x, y, z)
	return Float64(x + y)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Taylor expanded in z around 0 53.0%

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

   1. +-commutative 53.0%

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

4. Simplified 53.0%

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

5. Final simplification 53.0%

   \[\leadsto x + y \]

Alternative 9: 26.8% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Taylor expanded in x around inf 51.7%

   \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Step-by-step derivation

   1. *-commutative 51.7%

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

4. Simplified 51.7%

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

5. Taylor expanded in z around 0 26.6%

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

6. Final simplification 26.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))