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

Percentage Accurate: 100.0% → 99.0%

Time: 6.2s

Alternatives: 7

Speedup: 1.0×

• 20.7% 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: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right) \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (fma (- 1.0 z) y (* (- 1.0 z) x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return fma((1.0 - z), y, ((1.0 - z) * x));
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return fma(Float64(1.0 - z), y, Float64(Float64(1.0 - z) * x))
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * y + N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

4. Applied rewrites 99.2%

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

Alternative 2: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq -100:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;1 - z \leq 400000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)))
   (if (<= (- 1.0 z) -5e+104)
     t_0
     (if (<= (- 1.0 z) -100.0)
       (* (- z) y)
       (if (<= (- 1.0 z) 400000000.0) (+ y x) t_0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if ((1.0 - z) <= -5e+104) {
		tmp = t_0;
	} else if ((1.0 - z) <= -100.0) {
		tmp = -z * y;
	} else if ((1.0 - z) <= 400000000.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = -z * x
    if ((1.0d0 - z) <= (-5d+104)) then
        tmp = t_0
    else if ((1.0d0 - z) <= (-100.0d0)) then
        tmp = -z * y
    else if ((1.0d0 - z) <= 400000000.0d0) then
        tmp = y + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if ((1.0 - z) <= -5e+104) {
		tmp = t_0;
	} else if ((1.0 - z) <= -100.0) {
		tmp = -z * y;
	} else if ((1.0 - z) <= 400000000.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -z * x
	tmp = 0
	if (1.0 - z) <= -5e+104:
		tmp = t_0
	elif (1.0 - z) <= -100.0:
		tmp = -z * y
	elif (1.0 - z) <= 400000000.0:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(-z) * x)
	tmp = 0.0
	if (Float64(1.0 - z) <= -5e+104)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= -100.0)
		tmp = Float64(Float64(-z) * y);
	elseif (Float64(1.0 - z) <= 400000000.0)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -z * x;
	tmp = 0.0;
	if ((1.0 - z) <= -5e+104)
		tmp = t_0;
	elseif ((1.0 - z) <= -100.0)
		tmp = -z * y;
	elseif ((1.0 - z) <= 400000000.0)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * x), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+104], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], -100.0], N[((-z) * y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 400000000.0], N[(y + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -4.9999999999999997e104 or 4e8 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.8%

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

   if -4.9999999999999997e104 < (-.f64 #s(literal 1 binary64) z) < -100

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.5

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

   5. Applied rewrites 49.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 44.8%

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

   if -100 < (-.f64 #s(literal 1 binary64) z) < 4e8

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.4

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

   5. Applied rewrites 52.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.3%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. lower-+.f64 97.0

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

   11. Applied rewrites 97.0%

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

Alternative 3: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ \mathbf{if}\;z \leq -240000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+100}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)))
   (if (<= z -240000000.0)
     t_0
     (if (<= z 2.5e-9)
       (+ y x)
       (if (<= z 3.5e+49)
         (* (- 1.0 z) x)
         (if (<= z 4.8e+100) (* (- z) y) t_0))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if (z <= -240000000.0) {
		tmp = t_0;
	} else if (z <= 2.5e-9) {
		tmp = y + x;
	} else if (z <= 3.5e+49) {
		tmp = (1.0 - z) * x;
	} else if (z <= 4.8e+100) {
		tmp = -z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = -z * x
    if (z <= (-240000000.0d0)) then
        tmp = t_0
    else if (z <= 2.5d-9) then
        tmp = y + x
    else if (z <= 3.5d+49) then
        tmp = (1.0d0 - z) * x
    else if (z <= 4.8d+100) then
        tmp = -z * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if (z <= -240000000.0) {
		tmp = t_0;
	} else if (z <= 2.5e-9) {
		tmp = y + x;
	} else if (z <= 3.5e+49) {
		tmp = (1.0 - z) * x;
	} else if (z <= 4.8e+100) {
		tmp = -z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -z * x
	tmp = 0
	if z <= -240000000.0:
		tmp = t_0
	elif z <= 2.5e-9:
		tmp = y + x
	elif z <= 3.5e+49:
		tmp = (1.0 - z) * x
	elif z <= 4.8e+100:
		tmp = -z * y
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(-z) * x)
	tmp = 0.0
	if (z <= -240000000.0)
		tmp = t_0;
	elseif (z <= 2.5e-9)
		tmp = Float64(y + x);
	elseif (z <= 3.5e+49)
		tmp = Float64(Float64(1.0 - z) * x);
	elseif (z <= 4.8e+100)
		tmp = Float64(Float64(-z) * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -z * x;
	tmp = 0.0;
	if (z <= -240000000.0)
		tmp = t_0;
	elseif (z <= 2.5e-9)
		tmp = y + x;
	elseif (z <= 3.5e+49)
		tmp = (1.0 - z) * x;
	elseif (z <= 4.8e+100)
		tmp = -z * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * x), $MachinePrecision]}, If[LessEqual[z, -240000000.0], t$95$0, If[LessEqual[z, 2.5e-9], N[(y + x), $MachinePrecision], If[LessEqual[z, 3.5e+49], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 4.8e+100], N[((-z) * y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e8 or 4.80000000000000023e100 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.8%

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

   if -2.4e8 < z < 2.5000000000000001e-9

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.1

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

   5. Applied rewrites 52.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.9%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. lower-+.f64 97.5

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

   11. Applied rewrites 97.5%

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

   if 2.5000000000000001e-9 < z < 3.49999999999999975e49

   1. Initial program 99.7%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.0

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

   5. Applied rewrites 52.0%

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

   if 3.49999999999999975e49 < z < 4.80000000000000023e100

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   5. Applied rewrites 43.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 43.6%

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

Alternative 4: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -100 \lor \neg \left(1 - z \leq 400000000\right):\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -100.0) (not (<= (- 1.0 z) 400000000.0)))
   (* (- z) x)
   (+ y x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -100.0) || !((1.0 - z) <= 400000000.0)) {
		tmp = -z * x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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) <= (-100.0d0)) .or. (.not. ((1.0d0 - z) <= 400000000.0d0))) then
        tmp = -z * x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -100.0) || !((1.0 - z) <= 400000000.0)) {
		tmp = -z * x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -100.0) or not ((1.0 - z) <= 400000000.0):
		tmp = -z * x
	else:
		tmp = y + x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -100.0) || !(Float64(1.0 - z) <= 400000000.0))
		tmp = Float64(Float64(-z) * x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -100.0) || ~(((1.0 - z) <= 400000000.0)))
		tmp = -z * x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -100.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 400000000.0]], $MachinePrecision]], N[((-z) * x), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -100 or 4e8 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.9

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

   5. Applied rewrites 53.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.3%

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

   if -100 < (-.f64 #s(literal 1 binary64) z) < 4e8

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.4

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

   5. Applied rewrites 52.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.3%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. lower-+.f64 97.0

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

   11. Applied rewrites 97.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -100 \lor \neg \left(1 - z \leq 400000000\right):\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-285}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -4e-285) (* (- 1.0 z) x) (* (- 1.0 z) y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -4e-285) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 ((x + y) <= (-4d-285)) then
        tmp = (1.0d0 - z) * x
    else
        tmp = (1.0d0 - z) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -4e-285) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (x + y) <= -4e-285:
		tmp = (1.0 - z) * x
	else:
		tmp = (1.0 - z) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -4e-285)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(Float64(1.0 - z) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -4e-285)
		tmp = (1.0 - z) * x;
	else
		tmp = (1.0 - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e-285], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.0000000000000003e-285

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.3

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

   5. Applied rewrites 54.3%

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

   if -4.0000000000000003e-285 < (+.f64 x y)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.4

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

   5. Applied rewrites 52.4%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 7: 50.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ y + x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (+ y x))

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y + x
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return y + x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(y + x)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = y + x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 53.1

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

5. Applied rewrites 53.1%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 53.1%

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

9. Taylor expanded in z around 0

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

    1. +-commutative N/A

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

    2. lower-+.f64 52.3

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

11. Applied rewrites 52.3%

    \[\leadsto \color{blue}{y + x} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024337 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))