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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 6

Speedup: 1.0×

• 21.8% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return (1.0 - z) * (y + 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 = (1.0d0 - z) * (y + x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) \cdot x\\ \mathbf{if}\;1 - z \leq 0.9998:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 1.000001:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 z) x)))
   (if (<= (- 1.0 z) 0.9998)
     t_0
     (if (<= (- 1.0 z) 1.000001)
       (+ y x)
       (if (<= (- 1.0 z) 5e+14) t_0 (* (- z) y))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - z) * x;
	double tmp;
	if ((1.0 - z) <= 0.9998) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.000001) {
		tmp = y + x;
	} else if ((1.0 - z) <= 5e+14) {
		tmp = t_0;
	} else {
		tmp = -z * 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) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - z) * x
    if ((1.0d0 - z) <= 0.9998d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.000001d0) then
        tmp = y + x
    else if ((1.0d0 - z) <= 5d+14) then
        tmp = t_0
    else
        tmp = -z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - z) * x;
	double tmp;
	if ((1.0 - z) <= 0.9998) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.000001) {
		tmp = y + x;
	} else if ((1.0 - z) <= 5e+14) {
		tmp = t_0;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - z) * x
	tmp = 0
	if (1.0 - z) <= 0.9998:
		tmp = t_0
	elif (1.0 - z) <= 1.000001:
		tmp = y + x
	elif (1.0 - z) <= 5e+14:
		tmp = t_0
	else:
		tmp = -z * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - z) * x)
	tmp = 0.0
	if (Float64(1.0 - z) <= 0.9998)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.000001)
		tmp = Float64(y + x);
	elseif (Float64(1.0 - z) <= 5e+14)
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - z) * x;
	tmp = 0.0;
	if ((1.0 - z) <= 0.9998)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.000001)
		tmp = y + x;
	elseif ((1.0 - z) <= 5e+14)
		tmp = t_0;
	else
		tmp = -z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], 0.9998], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.000001], N[(y + x), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+14], t$95$0, N[((-z) * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) z) < 0.99980000000000002 or 1.00000099999999992 < (-.f64 #s(literal 1 binary64) z) < 5e14

   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. lower-*.f64 N/A

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

      2. lower--.f64 53.3

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

   5. Applied rewrites 53.3%

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

   if 0.99980000000000002 < (-.f64 #s(literal 1 binary64) z) < 1.00000099999999992

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-+.f64 99.0

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

   5. Applied rewrites 99.0%

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

   if 5e14 < (-.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 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 52.9

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

   5. Applied rewrites 52.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.9%

      \[\leadsto \left(-z\right) \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq 0.9998:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;1 - z \leq 1.000001:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))