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

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 8

Speedup: 1.0×

• 21.0% 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: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.62 \cdot 10^{-52} \lor \neg \left(y \leq 7 \cdot 10^{-12}\right) \land \left(y \leq 15500 \lor \neg \left(y \leq 2.06 \cdot 10^{+40}\right) \land y \leq 1.6 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 1.62e-52)
         (and (not (<= y 7e-12))
              (or (<= y 15500.0) (and (not (<= y 2.06e+40)) (<= y 1.6e+67)))))
   (* x (- 1.0 z))
   (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.62e-52) || (!(y <= 7e-12) && ((y <= 15500.0) || (!(y <= 2.06e+40) && (y <= 1.6e+67))))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * 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 ((y <= 1.62d-52) .or. (.not. (y <= 7d-12)) .and. (y <= 15500.0d0) .or. (.not. (y <= 2.06d+40)) .and. (y <= 1.6d+67)) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.62e-52) || (!(y <= 7e-12) && ((y <= 15500.0) || (!(y <= 2.06e+40) && (y <= 1.6e+67))))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 1.62e-52) or (not (y <= 7e-12) and ((y <= 15500.0) or (not (y <= 2.06e+40) and (y <= 1.6e+67)))):
		tmp = x * (1.0 - z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 1.62e-52) || (!(y <= 7e-12) && ((y <= 15500.0) || (!(y <= 2.06e+40) && (y <= 1.6e+67)))))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 1.62e-52) || (~((y <= 7e-12)) && ((y <= 15500.0) || (~((y <= 2.06e+40)) && (y <= 1.6e+67)))))
		tmp = x * (1.0 - z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 1.62e-52], And[N[Not[LessEqual[y, 7e-12]], $MachinePrecision], Or[LessEqual[y, 15500.0], And[N[Not[LessEqual[y, 2.06e+40]], $MachinePrecision], LessEqual[y, 1.6e+67]]]]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.61999999999999995e-52 or 7.0000000000000001e-12 < y < 15500 or 2.05999999999999999e40 < y < 1.59999999999999991e67

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.9%

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

   if 1.61999999999999995e-52 < y < 7.0000000000000001e-12 or 15500 < y < 2.05999999999999999e40 or 1.59999999999999991e67 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.4%

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

      1. sub-neg 86.4%

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

      2. distribute-lft-in 86.4%

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

      3. distribute-rgt-neg-out 86.4%

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

      4. unsub-neg 86.4%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot z} \]

      5. *-rgt-identity 86.4%

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

   4. Simplified 86.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.62 \cdot 10^{-52} \lor \neg \left(y \leq 7 \cdot 10^{-12}\right) \land \left(y \leq 15500 \lor \neg \left(y \leq 2.06 \cdot 10^{+40}\right) \land y \leq 1.6 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]

Alternative 3: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -4 \cdot 10^{+20} \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -4e+20) (not (<= (- 1.0 z) 2.0)))
   (* (+ x y) (- z))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -4e+20) || !((1.0 - z) <= 2.0)) {
		tmp = (x + y) * -z;
	} 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) <= (-4d+20)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = (x + y) * -z
    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) <= -4e+20) || !((1.0 - z) <= 2.0)) {
		tmp = (x + y) * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -4e+20) or not ((1.0 - z) <= 2.0):
		tmp = (x + y) * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -4e+20) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(Float64(x + y) * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -4e+20) || ~(((1.0 - z) <= 2.0)))
		tmp = (x + y) * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -4e+20], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -4e20 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 99.4%

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

      1. mul-1-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. distribute-rgt-neg-out 99.4%

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

      4. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   if -4e20 < (-.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%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -4 \cdot 10^{+20} \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq 1 \lor \neg \left(1 - z \leq 1.005\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) 1.0) (not (<= (- 1.0 z) 1.005)))
   (* x (- 1.0 z))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= 1.0) || !((1.0 - z) <= 1.005)) {
		tmp = x * (1.0 - z);
	} 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) <= 1.0d0) .or. (.not. ((1.0d0 - z) <= 1.005d0))) then
        tmp = x * (1.0d0 - z)
    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) <= 1.0) || !((1.0 - z) <= 1.005)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= 1.0) or not ((1.0 - z) <= 1.005):
		tmp = x * (1.0 - z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= 1.0) || !(Float64(1.0 - z) <= 1.005))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= 1.0) || ~(((1.0 - z) <= 1.005)))
		tmp = x * (1.0 - z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 1.005]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < 1 or 1.0049999999999999 < (-.f64 1 z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 49.0%

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

   if 1 < (-.f64 1 z) < 1.0049999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq 1 \lor \neg \left(1 - z \leq 1.005\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e-6)
   (* x (- 1.0 z))
   (if (<= z 3.55e-9) (+ x y) (- x (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-6) {
		tmp = x * (1.0 - z);
	} else if (z <= 3.55e-9) {
		tmp = x + y;
	} else {
		tmp = x - (x * 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 (z <= (-1.15d-6)) then
        tmp = x * (1.0d0 - z)
    else if (z <= 3.55d-9) then
        tmp = x + y
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-6) {
		tmp = x * (1.0 - z);
	} else if (z <= 3.55e-9) {
		tmp = x + y;
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e-6:
		tmp = x * (1.0 - z)
	elif z <= 3.55e-9:
		tmp = x + y
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e-6)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (z <= 3.55e-9)
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e-6)
		tmp = x * (1.0 - z);
	elseif (z <= 3.55e-9)
		tmp = x + y;
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e-6], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e-9], N[(x + y), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 55.9%

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

   if -1.15e-6 < z < 3.54999999999999994e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   if 3.54999999999999994e-9 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 47.9%

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

      1. sub-neg 47.9%

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

      2. +-commutative 47.9%

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

      3. distribute-rgt1-in 47.9%

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

      4. distribute-lft-neg-out 47.9%

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

      5. unsub-neg 47.9%

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

   4. Simplified 47.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 6: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -23.5 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -23.5) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -23.5) || !(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 <= (-23.5d0)) .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 <= -23.5) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -23.5) 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 <= -23.5) || !(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 <= -23.5) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -23.5], 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 < -23.5 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 52.7%

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

   3. Taylor expanded in z around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. distribute-rgt-neg-out 52.4%

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

   5. Simplified 52.4%

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

   if -23.5 < 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%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23.5 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 50.6% 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 52.3%

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

3. Final simplification 52.3%

   \[\leadsto x + y \]

Alternative 8: 26.0% 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 48.8%

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

3. Taylor expanded in z around 0 24.5%

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

4. Final simplification 24.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))