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

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 8

Speedup: 1.0×

• 20.9% 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: 98.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. +-commutative 98.4%

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

      3. distribute-rgt-neg-out 98.4%

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

      4. +-commutative 98.4%

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

   4. Simplified 98.4%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.8%

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

4. Final simplification 98.6%

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

Alternative 3: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -27.5 \lor \neg \left(z \leq 2.1 \cdot 10^{-7}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -27.5) (not (<= z 2.1e-7))) (- x (* x z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -27.5) || !(z <= 2.1e-7)) {
		tmp = x - (x * 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 ((z <= (-27.5d0)) .or. (.not. (z <= 2.1d-7))) then
        tmp = x - (x * 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 ((z <= -27.5) || !(z <= 2.1e-7)) {
		tmp = x - (x * z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -27.5) or not (z <= 2.1e-7):
		tmp = x - (x * z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -27.5) || !(z <= 2.1e-7))
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -27.5) || ~((z <= 2.1e-7)))
		tmp = x - (x * z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -27.5], N[Not[LessEqual[z, 2.1e-7]], $MachinePrecision]], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -27.5 or 2.1e-7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 57.3%

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

      1. sub-neg 57.3%

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

      2. +-commutative 57.3%

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

      3. distribute-rgt1-in 57.3%

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

      4. distribute-lft-neg-out 57.3%

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

      5. unsub-neg 57.3%

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

   4. Simplified 57.3%

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

   if -27.5 < z < 2.1e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -27.5 \lor \neg \left(z \leq 2.1 \cdot 10^{-7}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -410000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -410000000.0) (not (<= z 1.0))) (* z (- y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -410000000.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} 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 <= (-410000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -y
    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 <= -410000000.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -410000000.0) or not (z <= 1.0):
		tmp = z * -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -410000000.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -410000000.0) || ~((z <= 1.0)))
		tmp = z * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -410000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e8 or 1 < z

   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 93.1%

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

   3. Applied egg-rr 93.1%

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

   4. Taylor expanded in z around inf 92.9%

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

      1. associate-*r* 92.9%

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

      2. neg-mul-1 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in y around inf 48.8%

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

      1. associate-*r* 48.8%

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

      2. mul-1-neg 48.8%

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

   9. Simplified 48.8%

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

   if -4.1e8 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -410000000:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -410000000.0) (* z (- y)) (if (<= z 1.0) (+ x y) (* z (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -410000000.0) {
		tmp = z * -y;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = z * -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 <= (-410000000.0d0)) then
        tmp = z * -y
    else if (z <= 1.0d0) then
        tmp = x + y
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -410000000.0) {
		tmp = z * -y;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -410000000.0:
		tmp = z * -y
	elif z <= 1.0:
		tmp = x + y
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -410000000.0)
		tmp = Float64(z * Float64(-y));
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -410000000.0)
		tmp = z * -y;
	elseif (z <= 1.0)
		tmp = x + y;
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -410000000.0], N[(z * (-y)), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], N[(z * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e8

   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 93.0%

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

   3. Applied egg-rr 93.0%

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

   4. Taylor expanded in z around inf 93.0%

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

      1. associate-*r* 93.0%

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

      2. neg-mul-1 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in y around inf 54.4%

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

      1. associate-*r* 54.4%

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

      2. mul-1-neg 54.4%

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

   9. Simplified 54.4%

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

   if -4.1e8 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.0%

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

   if 1 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. +-commutative 99.5%

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

      3. distribute-rgt-neg-out 99.5%

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

      4. +-commutative 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in y around 0 61.1%

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

      1. associate-*r* 61.1%

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

      2. mul-1-neg 61.1%

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

   7. Simplified 61.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410000000:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e-59) (- x (* x z)) (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e-59) {
		tmp = x - (x * 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 <= (-1.1d-59)) then
        tmp = x - (x * 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 <= -1.1e-59) {
		tmp = x - (x * z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.1e-59:
		tmp = x - (x * z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e-59)
		tmp = Float64(x - Float64(x * 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 <= -1.1e-59)
		tmp = x - (x * z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e-59], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0999999999999999e-59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.2%

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

      1. sub-neg 80.2%

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

      2. +-commutative 80.2%

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

      3. distribute-rgt1-in 80.2%

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

      4. distribute-lft-neg-out 80.2%

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

      5. unsub-neg 80.2%

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

   4. Simplified 80.2%

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

   if -1.0999999999999999e-59 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 57.2%

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

      1. sub-neg 57.2%

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

      2. distribute-lft-in 57.2%

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

      3. distribute-rgt-neg-out 57.2%

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

      4. unsub-neg 57.2%

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

      5. *-rgt-identity 57.2%

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

   4. Simplified 57.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]

Alternative 7: 50.4% 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 54.5%

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

3. Final simplification 54.5%

   \[\leadsto x + y \]

Alternative 8: 26.5% 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. 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 96.9%

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

3. Applied egg-rr 96.9%

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

4. Taylor expanded in z around inf 71.1%

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

   1. associate-*r* 71.1%

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

   2. neg-mul-1 71.1%

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

6. Simplified 71.1%

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

7. Taylor expanded in z around 0 29.0%

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

8. Final simplification 29.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))