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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 9

Speedup: 1.0×

• 21.1% 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: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-143} \lor \neg \left(y \leq 3.8 \cdot 10^{-116}\right) \land y \leq 2.3 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 1.45e-143) (and (not (<= y 3.8e-116)) (<= y 2.3e-56)))
   (* x (- 1.0 z))
   (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.45e-143) || (!(y <= 3.8e-116) && (y <= 2.3e-56))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - 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 <= 1.45d-143) .or. (.not. (y <= 3.8d-116)) .and. (y <= 2.3d-56)) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.45e-143) || (!(y <= 3.8e-116) && (y <= 2.3e-56))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 1.45e-143) or (not (y <= 3.8e-116) and (y <= 2.3e-56)):
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 1.45e-143) || (!(y <= 3.8e-116) && (y <= 2.3e-56)))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 1.45e-143) || (~((y <= 3.8e-116)) && (y <= 2.3e-56)))
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 1.45e-143], And[N[Not[LessEqual[y, 3.8e-116]], $MachinePrecision], LessEqual[y, 2.3e-56]]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.45e-143 or 3.8000000000000001e-116 < y < 2.30000000000000002e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   if 1.45e-143 < y < 3.8000000000000001e-116 or 2.30000000000000002e-56 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-143} \lor \neg \left(y \leq 3.8 \cdot 10^{-116}\right) \land y \leq 2.3 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-116}:\\ \;\;\;\;y - y \cdot z\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 z))))
   (if (<= y 1.45e-143)
     t_0
     (if (<= y 3.8e-116)
       (- y (* y z))
       (if (<= y 3.9e-57) t_0 (* y (- 1.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (y <= 1.45e-143) {
		tmp = t_0;
	} else if (y <= 3.8e-116) {
		tmp = y - (y * z);
	} else if (y <= 3.9e-57) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - z)
    if (y <= 1.45d-143) then
        tmp = t_0
    else if (y <= 3.8d-116) then
        tmp = y - (y * z)
    else if (y <= 3.9d-57) then
        tmp = t_0
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (y <= 1.45e-143) {
		tmp = t_0;
	} else if (y <= 3.8e-116) {
		tmp = y - (y * z);
	} else if (y <= 3.9e-57) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - z)
	tmp = 0
	if y <= 1.45e-143:
		tmp = t_0
	elif y <= 3.8e-116:
		tmp = y - (y * z)
	elif y <= 3.9e-57:
		tmp = t_0
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (y <= 1.45e-143)
		tmp = t_0;
	elseif (y <= 3.8e-116)
		tmp = Float64(y - Float64(y * z));
	elseif (y <= 3.9e-57)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - z);
	tmp = 0.0;
	if (y <= 1.45e-143)
		tmp = t_0;
	elseif (y <= 3.8e-116)
		tmp = y - (y * z);
	elseif (y <= 3.9e-57)
		tmp = t_0;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.45e-143], t$95$0, If[LessEqual[y, 3.8e-116], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-57], t$95$0, N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.45e-143 or 3.8000000000000001e-116 < y < 3.90000000000000006e-57

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   if 1.45e-143 < y < 3.8000000000000001e-116

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 27.5%

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

      1. mul-1-neg 27.5%

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

   6. Simplified 27.5%

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

      1. unsub-neg 27.5%

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

   8. Applied egg-rr 27.5%

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

   if 3.90000000000000006e-57 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-116}:\\ \;\;\;\;y - y \cdot z\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 4: 97.9% 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 97.6%

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

      1. mul-1-neg 97.6%

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

      2. *-commutative 97.6%

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

      3. distribute-rgt-neg-out 97.6%

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

      4. +-commutative 97.6%

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

   4. Simplified 97.6%

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

   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 97.1%

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

      1. +-commutative 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 97.4%

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

Alternative 5: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-10} \lor \neg \left(z \leq 0.00012\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-10) (not (<= z 0.00012))) (* y (- 1.0 z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-10) || !(z <= 0.00012)) {
		tmp = y * (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 ((z <= (-3d-10)) .or. (.not. (z <= 0.00012d0))) then
        tmp = y * (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 ((z <= -3e-10) || !(z <= 0.00012)) {
		tmp = y * (1.0 - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-10) or not (z <= 0.00012):
		tmp = y * (1.0 - z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-10) || !(z <= 0.00012))
		tmp = Float64(y * 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 ((z <= -3e-10) || ~((z <= 0.00012)))
		tmp = y * (1.0 - z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-10], N[Not[LessEqual[z, 0.00012]], $MachinePrecision]], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e-10 or 1.20000000000000003e-4 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 53.8%

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

   if -3e-10 < z < 1.20000000000000003e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.4%

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

      1. +-commutative 99.4%

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

   4. Simplified 99.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-10} \lor \neg \left(z \leq 0.00012\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -330000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -330000.0) (not (<= z 1.0))) (* y (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -330000.0) || !(z <= 1.0)) {
		tmp = 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 ((z <= (-330000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = 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 ((z <= -330000.0) || !(z <= 1.0)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -330000.0) or not (z <= 1.0):
		tmp = y * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -330000.0) || !(z <= 1.0))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -330000.0) || ~((z <= 1.0)))
		tmp = y * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -330000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e5 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 55.0%

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

      1. mul-1-neg 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in z 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. neg-mul-1 54.4%

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

   9. Simplified 54.4%

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

   if -3.3e5 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.1%

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

      1. +-commutative 95.1%

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

   4. Simplified 95.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -330000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 32.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.5e-59) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e-59) {
		tmp = x;
	} else {
		tmp = 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 (y <= 1.5d-59) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e-59) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.5e-59:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.5e-59)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.5e-59)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.5e-59], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.5e-59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in z around 0 32.2%

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

   if 1.5e-59 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.3%

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

   3. Taylor expanded in z around 0 38.3%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 51.3% 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 47.7%

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

   1. +-commutative 47.7%

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

4. Simplified 47.7%

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

5. Final simplification 47.7%

   \[\leadsto x + y \]

Alternative 9: 26.7% 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 50.8%

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

   1. *-commutative 50.8%

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

4. Simplified 50.8%

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

5. Taylor expanded in z around 0 25.5%

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

6. Final simplification 25.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))