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

Percentage Accurate: 100.0% → 98.9%

Time: 4.4s

Alternatives: 10

Speedup: 1.0×

• 20.8% 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: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right) \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (fma (- 1.0 z) y (* (- 1.0 z) x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return fma((1.0 - z), y, ((1.0 - z) * x));
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return fma(Float64(1.0 - z), y, Float64(Float64(1.0 - z) * x))
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * y + N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

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 98.4%

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

   4. fma-def 98.4%

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

4. Applied egg-rr 98.4%

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

5. Final simplification 98.4%

   \[\leadsto \mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right) \]
6. Add Preprocessing

Alternative 2: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(1 - z\right) \cdot y\\ t_1 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -1 \cdot 10^{+238}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;1 - z \leq -400:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 z) y)) (t_1 (* z (- x))))
   (if (<= (- 1.0 z) -1e+238)
     (* z (- y))
     (if (<= (- 1.0 z) -5e+186)
       t_1
       (if (<= (- 1.0 z) -400.0)
         t_0
         (if (<= (- 1.0 z) 1.0)
           (+ y x)
           (if (<= (- 1.0 z) 5e+171) t_0 t_1)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (1.0 - z) * y;
	double t_1 = z * -x;
	double tmp;
	if ((1.0 - z) <= -1e+238) {
		tmp = z * -y;
	} else if ((1.0 - z) <= -5e+186) {
		tmp = t_1;
	} else if ((1.0 - z) <= -400.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0) {
		tmp = y + x;
	} else if ((1.0 - z) <= 5e+171) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = (1.0d0 - z) * y
    t_1 = z * -x
    if ((1.0d0 - z) <= (-1d+238)) then
        tmp = z * -y
    else if ((1.0d0 - z) <= (-5d+186)) then
        tmp = t_1
    else if ((1.0d0 - z) <= (-400.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.0d0) then
        tmp = y + x
    else if ((1.0d0 - z) <= 5d+171) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = (1.0 - z) * y;
	double t_1 = z * -x;
	double tmp;
	if ((1.0 - z) <= -1e+238) {
		tmp = z * -y;
	} else if ((1.0 - z) <= -5e+186) {
		tmp = t_1;
	} else if ((1.0 - z) <= -400.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0) {
		tmp = y + x;
	} else if ((1.0 - z) <= 5e+171) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (1.0 - z) * y
	t_1 = z * -x
	tmp = 0
	if (1.0 - z) <= -1e+238:
		tmp = z * -y
	elif (1.0 - z) <= -5e+186:
		tmp = t_1
	elif (1.0 - z) <= -400.0:
		tmp = t_0
	elif (1.0 - z) <= 1.0:
		tmp = y + x
	elif (1.0 - z) <= 5e+171:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(1.0 - z) * y)
	t_1 = Float64(z * Float64(-x))
	tmp = 0.0
	if (Float64(1.0 - z) <= -1e+238)
		tmp = Float64(z * Float64(-y));
	elseif (Float64(1.0 - z) <= -5e+186)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= -400.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.0)
		tmp = Float64(y + x);
	elseif (Float64(1.0 - z) <= 5e+171)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (1.0 - z) * y;
	t_1 = z * -x;
	tmp = 0.0;
	if ((1.0 - z) <= -1e+238)
		tmp = z * -y;
	elseif ((1.0 - z) <= -5e+186)
		tmp = t_1;
	elseif ((1.0 - z) <= -400.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.0)
		tmp = y + x;
	elseif ((1.0 - z) <= 5e+171)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+238], N[(z * (-y)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+186], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], -400.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0], N[(y + x), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+171], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 z) < -1e238

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 48.8%

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

   4. Taylor expanded in z around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. *-commutative 48.8%

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

      3. distribute-rgt-neg-in 48.8%

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

   6. Simplified 48.8%

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

   if -1e238 < (-.f64 1 z) < -4.99999999999999954e186 or 5.0000000000000004e171 < (-.f64 1 z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 50.1%

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

      1. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

   8. Simplified 50.1%

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

   if -4.99999999999999954e186 < (-.f64 1 z) < -400 or 1 < (-.f64 1 z) < 5.0000000000000004e171

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 41.6%

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

   if -400 < (-.f64 1 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 98.8%

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

      1. +-commutative 98.8%

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

   5. Simplified 98.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -1 \cdot 10^{+238}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq -400:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+171}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+172}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -130:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+185} \lor \neg \left(z \leq 2.8 \cdot 10^{+237}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* z (- y))))
   (if (<= z -2.15e+172)
     t_0
     (if (<= z -130.0)
       t_1
       (if (<= z 1.0)
         (+ y x)
         (if (or (<= z 1.26e+185) (not (<= z 2.8e+237))) t_1 t_0))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = z * -y;
	double tmp;
	if (z <= -2.15e+172) {
		tmp = t_0;
	} else if (z <= -130.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = y + x;
	} else if ((z <= 1.26e+185) || !(z <= 2.8e+237)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = z * -x
    t_1 = z * -y
    if (z <= (-2.15d+172)) then
        tmp = t_0
    else if (z <= (-130.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = y + x
    else if ((z <= 1.26d+185) .or. (.not. (z <= 2.8d+237))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = z * -y;
	double tmp;
	if (z <= -2.15e+172) {
		tmp = t_0;
	} else if (z <= -130.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = y + x;
	} else if ((z <= 1.26e+185) || !(z <= 2.8e+237)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = z * -x
	t_1 = z * -y
	tmp = 0
	if z <= -2.15e+172:
		tmp = t_0
	elif z <= -130.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = y + x
	elif (z <= 1.26e+185) or not (z <= 2.8e+237):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (z <= -2.15e+172)
		tmp = t_0;
	elseif (z <= -130.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(y + x);
	elseif ((z <= 1.26e+185) || !(z <= 2.8e+237))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = z * -y;
	tmp = 0.0;
	if (z <= -2.15e+172)
		tmp = t_0;
	elseif (z <= -130.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = y + x;
	elseif ((z <= 1.26e+185) || ~((z <= 2.8e+237)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[z, -2.15e+172], t$95$0, If[LessEqual[z, -130.0], t$95$1, If[LessEqual[z, 1.0], N[(y + x), $MachinePrecision], If[Or[LessEqual[z, 1.26e+185], N[Not[LessEqual[z, 2.8e+237]], $MachinePrecision]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1500000000000001e172 or 1.26e185 < z < 2.79999999999999983e237

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 50.1%

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

      1. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

   8. Simplified 50.1%

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

   if -2.1500000000000001e172 < z < -130 or 1 < z < 1.26e185 or 2.79999999999999983e237 < 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 42.3%

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

   4. Taylor expanded in z around inf 41.2%

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

      1. mul-1-neg 41.2%

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

      2. *-commutative 41.2%

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

      3. distribute-rgt-neg-in 41.2%

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

   6. Simplified 41.2%

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

   if -130 < 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 97.5%

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

      1. +-commutative 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+172}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -130:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+185} \lor \neg \left(z \leq 2.8 \cdot 10^{+237}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -400 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -400.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- y) x))
   (+ y x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -400.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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) <= (-400.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-y - x)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -400.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -400.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-y - x)
	else:
		tmp = y + x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -400.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-y) - x));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -400.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-y - x);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -400.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -400 or 2 < (-.f64 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 98.0%

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

      1. associate-*r* 98.0%

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

      2. neg-mul-1 98.0%

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

      3. *-commutative 98.0%

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

      4. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   if -400 < (-.f64 1 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 97.5%

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

      1. +-commutative 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -400 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.75e+24) (not (<= z 1.0))) (* z (- x)) (+ y x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+24) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-1.75d+24)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+24) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.75e+24) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = y + x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.75e+24) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.75e+24) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.75e+24], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e24 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in z around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-commutative 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

   8. Simplified 58.2%

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

   if -1.7500000000000001e24 < 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 95.4%

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

      1. +-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-101}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 1.5e-101) (* (- 1.0 z) x) (* (- 1.0 z) y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e-101) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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-101) then
        tmp = (1.0d0 - z) * x
    else
        tmp = (1.0d0 - z) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e-101) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 1.5e-101:
		tmp = (1.0 - z) * x
	else:
		tmp = (1.0 - z) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 1.5e-101)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(Float64(1.0 - z) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.5e-101)
		tmp = (1.0 - z) * x;
	else
		tmp = (1.0 - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 1.5e-101], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5000000000000002e-101

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   if 1.5000000000000002e-101 < 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 66.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-101}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* (- 1.0 z) (+ y x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (1.0 - z) * (y + x);
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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) * (y + x)
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (1.0 - z) * (y + x)

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(1.0 - z) * Float64(y + x))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (1.0 - z) * (y + x);
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * N[(y + x), $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%

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

Alternative 8: 42.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.08 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y 1.08e-103) x y))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.08e-103) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= 1.08d-103) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.08e-103) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 1.08e-103:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 1.08e-103)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.08e-103)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 1.08e-103], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.0799999999999999e-103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in z around 0 29.4%

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

   if 1.0799999999999999e-103 < 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 66.6%

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

   4. Taylor expanded in z around 0 34.9%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.08 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ y + x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (+ y x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return y + x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y + x
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return y + x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(y + x)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = y + x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(y + x), $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 48.3%

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

   1. +-commutative 48.3%

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

5. Simplified 48.3%

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

6. Final simplification 48.3%

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

Alternative 10: 26.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 54.6%

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

   1. *-commutative 54.6%

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

5. Simplified 54.6%

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

6. Taylor expanded in z around 0 25.2%

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

7. Final simplification 25.2%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))