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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 7

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 52.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \leq 1\\ \mathbf{if}\;1 - z \leq -3 \cdot 10^{+191}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;t\_0 \lor \neg t\_0:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (<= (- 1.0 z) 1.0)))
   (if (<= (- 1.0 z) -3e+191)
     (* y (- z))
     (if (<= (- 1.0 z) -5e+59)
       (* z (- x))
       (if (or t_0 (not t_0)) (* y (- 1.0 z)) (+ x y))))))

C

double code(double x, double y, double z) {
	int t_0 = (1.0 - z) <= 1.0;
	double tmp;
	if ((1.0 - z) <= -3e+191) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -5e+59) {
		tmp = z * -x;
	} else if (t_0 || !t_0) {
		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
    logical :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - z) <= 1.0d0
    if ((1.0d0 - z) <= (-3d+191)) then
        tmp = y * -z
    else if ((1.0d0 - z) <= (-5d+59)) then
        tmp = z * -x
    else if (t_0 .or. (.not. t_0)) 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) {
	boolean t_0 = (1.0 - z) <= 1.0;
	double tmp;
	if ((1.0 - z) <= -3e+191) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -5e+59) {
		tmp = z * -x;
	} else if (t_0 || !t_0) {
		tmp = y * (1.0 - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - z) <= 1.0
	tmp = 0
	if (1.0 - z) <= -3e+191:
		tmp = y * -z
	elif (1.0 - z) <= -5e+59:
		tmp = z * -x
	elif t_0 or not t_0:
		tmp = y * (1.0 - z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - z) <= 1.0
	tmp = 0.0
	if (Float64(1.0 - z) <= -3e+191)
		tmp = Float64(y * Float64(-z));
	elseif (Float64(1.0 - z) <= -5e+59)
		tmp = Float64(z * Float64(-x));
	elseif (t_0 || !t_0)
		tmp = Float64(y * Float64(1.0 - z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - z) <= 1.0;
	tmp = 0.0;
	if ((1.0 - z) <= -3e+191)
		tmp = y * -z;
	elseif ((1.0 - z) <= -5e+59)
		tmp = z * -x;
	elseif (t_0 || ~(t_0))
		tmp = y * (1.0 - z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = LessEqual[N[(1.0 - z), $MachinePrecision], 1.0]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -3e+191], N[(y * (-z)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+59], N[(z * (-x)), $MachinePrecision], If[Or[t$95$0, N[Not[t$95$0], $MachinePrecision]], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -2.9999999999999997e191

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. mul-1-neg 100.0%

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

      4. mul-1-neg 100.0%

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

      5. neg-sub0 100.0%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(x + y\right)\right)} \]

      6. associate--r+ 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(0 - x\right) - y\right)} \]

      7. neg-sub0 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-rgt-neg-in 45.3%

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

   8. Simplified 45.3%

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

   if -2.9999999999999997e191 < (-.f64 #s(literal 1 binary64) z) < -4.9999999999999997e59

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. mul-1-neg 100.0%

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

      4. mul-1-neg 100.0%

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

      5. neg-sub0 100.0%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(x + y\right)\right)} \]

      6. associate--r+ 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(0 - x\right) - y\right)} \]

      7. neg-sub0 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-rgt-neg-in 50.6%

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

   8. Simplified 50.6%

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

   if -4.9999999999999997e59 < (-.f64 #s(literal 1 binary64) z) < 1 or 1 < (-.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 54.8%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 47.2%

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

      1. +-commutative 47.2%

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

   5. Simplified 47.2%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -3 \cdot 10^{+191}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 1 \lor \neg \left(1 - z \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -55:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+57} \lor \neg \left(z \leq 2.6 \cdot 10^{+191}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= z -55.0)
     t_0
     (if (<= z 1.0)
       (+ x y)
       (if (or (<= z 1.05e+57) (not (<= z 2.6e+191))) t_0 (* z (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -55.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 1.05e+57) || !(z <= 2.6e+191)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * -z
    if (z <= (-55.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 1.05d+57) .or. (.not. (z <= 2.6d+191))) then
        tmp = t_0
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -55.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 1.05e+57) || !(z <= 2.6e+191)) {
		tmp = t_0;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if z <= -55.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 1.05e+57) or not (z <= 2.6e+191):
		tmp = t_0
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -55.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 1.05e+57) || !(z <= 2.6e+191))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (z <= -55.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 1.05e+57) || ~((z <= 2.6e+191)))
		tmp = t_0;
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -55.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1.05e+57], N[Not[LessEqual[z, 2.6e+191]], $MachinePrecision]], t$95$0, N[(z * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -55 or 1 < z < 1.04999999999999995e57 or 2.6e191 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. distribute-rgt-neg-in 98.1%

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

      3. mul-1-neg 98.1%

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

      4. mul-1-neg 98.1%

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

      5. neg-sub0 98.1%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(x + y\right)\right)} \]

      6. associate--r+ 98.1%

         \[\leadsto z \cdot \color{blue}{\left(\left(0 - x\right) - y\right)} \]

      7. neg-sub0 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in x around 0 47.1%

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

      1. mul-1-neg 47.1%

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

      2. distribute-rgt-neg-in 47.1%

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

   8. Simplified 47.1%

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

   if -55 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   if 1.04999999999999995e57 < z < 2.6e191

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. mul-1-neg 100.0%

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

      4. mul-1-neg 100.0%

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

      5. neg-sub0 100.0%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(x + y\right)\right)} \]

      6. associate--r+ 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(0 - x\right) - y\right)} \]

      7. neg-sub0 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-rgt-neg-in 50.6%

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

   8. Simplified 50.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -55:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+57} \lor \neg \left(z \leq 2.6 \cdot 10^{+191}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -200000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -200000.0) (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) <= -200000.0) || !((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) <= (-200000.0d0)) .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) <= -200000.0) || !((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) <= -200000.0) 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) <= -200000.0) || !(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) <= -200000.0) || ~(((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], -200000.0], 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 #s(literal 1 binary64) z) < -2e5 or 2 < (-.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 z around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-in 98.5%

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

      3. mul-1-neg 98.5%

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

      4. mul-1-neg 98.5%

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

      5. neg-sub0 98.5%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(x + y\right)\right)} \]

      6. associate--r+ 98.5%

         \[\leadsto z \cdot \color{blue}{\left(\left(0 - x\right) - y\right)} \]

      7. neg-sub0 98.5%

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

   5. Simplified 98.5%

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

   if -2e5 < (-.f64 #s(literal 1 binary64) z) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -200000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+21} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.14e+21) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.14e+21) || !(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 <= (-1.14d+21)) .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 <= -1.14e+21) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.14e+21) 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 <= -1.14e+21) || !(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 <= -1.14e+21) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.14e+21], 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 < -1.14e21 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. distribute-rgt-neg-in 98.6%

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

      3. mul-1-neg 98.6%

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

      4. mul-1-neg 98.6%

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

      5. neg-sub0 98.6%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(x + y\right)\right)} \]

      6. associate--r+ 98.6%

         \[\leadsto z \cdot \color{blue}{\left(\left(0 - x\right) - y\right)} \]

      7. neg-sub0 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in x around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. distribute-rgt-neg-in 56.5%

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

   8. Simplified 56.5%

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

   if -1.14e21 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.2%

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

      1. +-commutative 96.2%

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

   5. Simplified 96.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+21} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.9e-125) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.9e-125) {
		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 <= 1.9d-125) 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 <= 1.9e-125) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.9e-125:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.9e-125)
		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 <= 1.9e-125)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.9e-125], 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 < 1.9000000000000001e-125

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.8%

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

      1. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if 1.9000000000000001e-125 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Taylor expanded in z around 0 47.2%

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

   1. +-commutative 47.2%

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

5. Simplified 47.2%

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

6. Final simplification 47.2%

   \[\leadsto x + y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))