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

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 9

Speedup: 1.0×

• 21.3% 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: 74.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 1.0000005:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+188} \lor \neg \left(1 - z \leq 4 \cdot 10^{+212}\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= (- 1.0 z) -5e+152)
     (* y (- z))
     (if (<= (- 1.0 z) -5.0)
       t_0
       (if (<= (- 1.0 z) 1.0000005)
         (+ x y)
         (if (or (<= (- 1.0 z) 5e+188) (not (<= (- 1.0 z) 4e+212)))
           (* y (- 1.0 z))
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if ((1.0 - z) <= -5e+152) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -5.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0000005) {
		tmp = x + y;
	} else if (((1.0 - z) <= 5e+188) || !((1.0 - z) <= 4e+212)) {
		tmp = y * (1.0 - z);
	} else {
		tmp = t_0;
	}
	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 = z * -x
    if ((1.0d0 - z) <= (-5d+152)) then
        tmp = y * -z
    else if ((1.0d0 - z) <= (-5.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.0000005d0) then
        tmp = x + y
    else if (((1.0d0 - z) <= 5d+188) .or. (.not. ((1.0d0 - z) <= 4d+212))) then
        tmp = y * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if ((1.0 - z) <= -5e+152) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -5.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0000005) {
		tmp = x + y;
	} else if (((1.0 - z) <= 5e+188) || !((1.0 - z) <= 4e+212)) {
		tmp = y * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if (1.0 - z) <= -5e+152:
		tmp = y * -z
	elif (1.0 - z) <= -5.0:
		tmp = t_0
	elif (1.0 - z) <= 1.0000005:
		tmp = x + y
	elif ((1.0 - z) <= 5e+188) or not ((1.0 - z) <= 4e+212):
		tmp = y * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (Float64(1.0 - z) <= -5e+152)
		tmp = Float64(y * Float64(-z));
	elseif (Float64(1.0 - z) <= -5.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.0000005)
		tmp = Float64(x + y);
	elseif ((Float64(1.0 - z) <= 5e+188) || !(Float64(1.0 - z) <= 4e+212))
		tmp = Float64(y * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if ((1.0 - z) <= -5e+152)
		tmp = y * -z;
	elseif ((1.0 - z) <= -5.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.0000005)
		tmp = x + y;
	elseif (((1.0 - z) <= 5e+188) || ~(((1.0 - z) <= 4e+212)))
		tmp = y * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+152], N[(y * (-z)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], -5.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0000005], N[(x + y), $MachinePrecision], If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+188], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 4e+212]], $MachinePrecision]], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -5e152

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. 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 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in z around inf 95.7%

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

      1. mul-1-neg 95.7%

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

      2. distribute-rgt-neg-in 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in y around inf 45.2%

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

      1. associate-*r* 45.2%

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

      2. neg-mul-1 45.2%

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

   10. Simplified 45.2%

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

   if -5e152 < (-.f64 #s(literal 1 binary64) z) < -5 or 5.0000000000000001e188 < (-.f64 #s(literal 1 binary64) z) < 3.9999999999999996e212

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. 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 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 63.8%

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

   6. Taylor expanded in z around inf 60.4%

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

      1. associate-*r* 60.4%

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

      2. neg-mul-1 60.4%

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

   8. Simplified 60.4%

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

   if -5 < (-.f64 #s(literal 1 binary64) z) < 1.0000005000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.8%

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

      1. +-commutative 98.8%

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

   5. Simplified 98.8%

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

   if 1.0000005000000001 < (-.f64 #s(literal 1 binary64) z) < 5.0000000000000001e188 or 3.9999999999999996e212 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 45.2%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 1.0000005:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+188} \lor \neg \left(1 - z \leq 4 \cdot 10^{+212}\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+213}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1880000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))) (t_1 (* z (- x))))
   (if (<= z -9.2e+213)
     t_0
     (if (<= z -5.2e+190)
       t_1
       (if (<= z -1880000.0)
         t_0
         (if (<= z 1.0) (+ x y) (if (<= z 5.8e+149) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double t_1 = z * -x;
	double tmp;
	if (z <= -9.2e+213) {
		tmp = t_0;
	} else if (z <= -5.2e+190) {
		tmp = t_1;
	} else if (z <= -1880000.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if (z <= 5.8e+149) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y * -z
    t_1 = z * -x
    if (z <= (-9.2d+213)) then
        tmp = t_0
    else if (z <= (-5.2d+190)) then
        tmp = t_1
    else if (z <= (-1880000.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if (z <= 5.8d+149) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double t_1 = z * -x;
	double tmp;
	if (z <= -9.2e+213) {
		tmp = t_0;
	} else if (z <= -5.2e+190) {
		tmp = t_1;
	} else if (z <= -1880000.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if (z <= 5.8e+149) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	t_1 = z * -x
	tmp = 0
	if z <= -9.2e+213:
		tmp = t_0
	elif z <= -5.2e+190:
		tmp = t_1
	elif z <= -1880000.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif z <= 5.8e+149:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	t_1 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -9.2e+213)
		tmp = t_0;
	elseif (z <= -5.2e+190)
		tmp = t_1;
	elseif (z <= -1880000.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif (z <= 5.8e+149)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	t_1 = z * -x;
	tmp = 0.0;
	if (z <= -9.2e+213)
		tmp = t_0;
	elseif (z <= -5.2e+190)
		tmp = t_1;
	elseif (z <= -1880000.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif (z <= 5.8e+149)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -9.2e+213], t$95$0, If[LessEqual[z, -5.2e+190], t$95$1, If[LessEqual[z, -1880000.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.8e+149], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999992e213 or -5.20000000000000022e190 < z < -1.88e6 or 5.8000000000000004e149 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. 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 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in z around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. distribute-rgt-neg-in 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in y around inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

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

   10. Simplified 44.4%

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

   if -9.19999999999999992e213 < z < -5.20000000000000022e190 or 1 < z < 5.8000000000000004e149

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. 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 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 63.8%

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

   6. Taylor expanded in z around inf 60.4%

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

      1. associate-*r* 60.4%

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

      2. neg-mul-1 60.4%

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

   8. Simplified 60.4%

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

   if -1.88e6 < 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 97.2%

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

      1. +-commutative 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+190}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1880000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-104} \lor \neg \left(y \leq 450000000\right) \land y \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 1.7e-104) (and (not (<= y 450000000.0)) (<= y 4.5e+57)))
   (* x (- 1.0 z))
   (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.7e-104) || (!(y <= 450000000.0) && (y <= 4.5e+57))) {
		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 <= 1.7d-104) .or. (.not. (y <= 450000000.0d0)) .and. (y <= 4.5d+57)) 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 <= 1.7e-104) || (!(y <= 450000000.0) && (y <= 4.5e+57))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 1.7e-104) or (not (y <= 450000000.0) and (y <= 4.5e+57)):
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 1.7e-104) || (!(y <= 450000000.0) && (y <= 4.5e+57)))
		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 <= 1.7e-104) || (~((y <= 450000000.0)) && (y <= 4.5e+57)))
		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, 1.7e-104], And[N[Not[LessEqual[y, 450000000.0]], $MachinePrecision], LessEqual[y, 4.5e+57]]], 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 < 1.70000000000000008e-104 or 4.5e8 < y < 4.49999999999999996e57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   if 1.70000000000000008e-104 < y < 4.5e8 or 4.49999999999999996e57 < 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 72.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-104} \lor \neg \left(y \leq 450000000\right) \land y \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -5.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- x) y))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -5.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-x - 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 (((1.0d0 - z) <= (-5.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-x - 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 (((1.0 - z) <= -5.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-x - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -5.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-x - y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -5.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-x) - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -5.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-x - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -5.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -5 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 96.9%

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

      1. mul-1-neg 96.9%

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

      2. distribute-lft-neg-out 96.9%

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

      3. *-commutative 96.9%

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

      4. +-commutative 96.9%

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

   5. Simplified 96.9%

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

   if -5 < (-.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 97.9%

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

      1. +-commutative 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 97.4%

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

Alternative 6: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -58 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -58.0) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -58.0) || !(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 <= (-58.0d0)) .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 <= -58.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -58.0) 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 <= -58.0) || !(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 <= -58.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -58.0], 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 < -58 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. 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%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 65.9%

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

   6. Taylor expanded in z around inf 64.0%

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

      1. associate-*r* 64.0%

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

      2. neg-mul-1 64.0%

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

   8. Simplified 64.0%

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

   if -58 < 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 97.9%

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

      1. +-commutative 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -58 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 31.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.15e-86) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.15e-86) {
		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 <= 1.15d-86) 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 <= 1.15e-86) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.15e-86:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.15e-86)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.15e-86)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.15e-86], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.14999999999999998e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in z around 0 33.8%

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

   if 1.14999999999999998e-86 < 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 67.3%

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

   4. Taylor expanded in z around 0 40.4%

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

Alternative 8: 49.9% 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 52.3%

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

   1. +-commutative 52.3%

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

5. Simplified 52.3%

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

6. Final simplification 52.3%

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

Alternative 9: 25.3% 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. Add Preprocessing

3. Taylor expanded in x around inf 58.1%

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

   1. *-commutative 58.1%

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

5. Simplified 58.1%

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

6. Taylor expanded in z around 0 27.0%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))