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

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 8

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: 100.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in z around inf 100.0%

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

   1. +-commutative 100.0%

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

   2. mul-1-neg 100.0%

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

   3. unsub-neg 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -0.4 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(y + x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -0.4) (not (<= (- 1.0 z) 2.0)))
   (* (+ y x) (- z))
   (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -0.4) || !((1.0 - z) <= 2.0)) {
		tmp = (y + x) * -z;
	} else {
		tmp = y + x;
	}
	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) <= (-0.4d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = (y + x) * -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -0.4) || !((1.0 - z) <= 2.0)) {
		tmp = (y + x) * -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -0.4) or not ((1.0 - z) <= 2.0):
		tmp = (y + x) * -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -0.4) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(Float64(y + x) * Float64(-z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -0.4) || ~(((1.0 - z) <= 2.0)))
		tmp = (y + x) * -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -0.4], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] * (-z)), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -0.40000000000000002 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 99.0%

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

      1. mul-1-neg 99.0%

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

      2. +-commutative 99.0%

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

      3. distribute-rgt-neg-out 99.0%

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

      4. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   if -0.40000000000000002 < (-.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 97.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -0.4 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(y + x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -0.4 \lor \neg \left(1 - z \leq 1.1\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -0.4) (not (<= (- 1.0 z) 1.1)))
   (* x (- 1.0 z))
   (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -0.4) || !((1.0 - z) <= 1.1)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y + x;
	}
	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) <= (-0.4d0)) .or. (.not. ((1.0d0 - z) <= 1.1d0))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -0.4) || !((1.0 - z) <= 1.1)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -0.4) or not ((1.0 - z) <= 1.1):
		tmp = x * (1.0 - z)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -0.4) || !(Float64(1.0 - z) <= 1.1))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -0.4) || ~(((1.0 - z) <= 1.1)))
		tmp = x * (1.0 - z);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -0.4], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 1.1]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -0.40000000000000002 or 1.1000000000000001 < (-.f64 1 z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 55.1%

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

   if -0.40000000000000002 < (-.f64 1 z) < 1.1000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -0.4 \lor \neg \left(1 - z \leq 1.1\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+14) (not (<= z 1.0))) (* x (- z)) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+14) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = y + x;
	}
	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 <= (-6d+14)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+14) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+14) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+14) || !(z <= 1.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e+14) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+14], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e14 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 54.8%

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

      1. sub-neg 54.8%

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

      2. +-commutative 54.8%

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

      3. distribute-rgt1-in 54.8%

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

      4. distribute-lft-neg-out 54.8%

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

      5. unsub-neg 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in z around inf 54.2%

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

      1. associate-*r* 54.2%

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

      2. mul-1-neg 54.2%

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

   7. Simplified 54.2%

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

   if -6e14 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e-111) (* x (- 1.0 z)) (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e-111) {
		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 (x <= (-1.2d-111)) 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 (x <= -1.2e-111) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e-111:
		tmp = x * (1.0 - z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e-111)
		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 (x <= -1.2e-111)
		tmp = x * (1.0 - z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e-111], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e-111

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 72.5%

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

   if -1.2e-111 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 56.5%

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

      1. sub-neg 56.5%

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

      2. distribute-lft-in 56.5%

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

      3. distribute-rgt-neg-out 56.5%

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

      4. unsub-neg 56.5%

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

      5. *-rgt-identity 56.5%

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

   4. Simplified 56.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 7: 50.7% accurate, 2.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in z around 0 50.6%

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

3. Final simplification 50.6%

   \[\leadsto y + x \]

Alternative 8: 25.6% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

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 99.6%

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

3. Applied egg-rr 99.6%

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

4. Taylor expanded in z around inf 73.3%

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

   1. mul-1-neg 73.3%

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

   2. distribute-rgt-neg-in 73.3%

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

6. Simplified 73.3%

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

7. Taylor expanded in z around 0 24.9%

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

8. Final simplification 24.9%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))