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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 10

Speedup: 1.0×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

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

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

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

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (- 1.0 z) (+ x y)))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 - z) * (x + y)
end function

Java

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

Python

def code(x, y, z):
	return (1.0 - z) * (x + y)

Julia

function code(x, y, z)
	return Float64(Float64(1.0 - z) * Float64(x + y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 - z) * (x + y);
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq 0.98:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1.05:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))))
   (if (<= (- 1.0 z) 0.98)
     t_0
     (if (<= (- 1.0 z) 1.05)
       (+ x y)
       (if (<= (- 1.0 z) 1e+57)
         t_0
         (if (<= (- 1.0 z) 5e+207) (* x (- z)) (* y (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= 0.98) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.05) {
		tmp = x + y;
	} else if ((1.0 - z) <= 1e+57) {
		tmp = t_0;
	} else if ((1.0 - z) <= 5e+207) {
		tmp = x * -z;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    if ((1.0d0 - z) <= 0.98d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.05d0) then
        tmp = x + y
    else if ((1.0d0 - z) <= 1d+57) then
        tmp = t_0
    else if ((1.0d0 - z) <= 5d+207) then
        tmp = x * -z
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= 0.98) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.05) {
		tmp = x + y;
	} else if ((1.0 - z) <= 1e+57) {
		tmp = t_0;
	} else if ((1.0 - z) <= 5e+207) {
		tmp = x * -z;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	tmp = 0
	if (1.0 - z) <= 0.98:
		tmp = t_0
	elif (1.0 - z) <= 1.05:
		tmp = x + y
	elif (1.0 - z) <= 1e+57:
		tmp = t_0
	elif (1.0 - z) <= 5e+207:
		tmp = x * -z
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (Float64(1.0 - z) <= 0.98)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.05)
		tmp = Float64(x + y);
	elseif (Float64(1.0 - z) <= 1e+57)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 5e+207)
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	tmp = 0.0;
	if ((1.0 - z) <= 0.98)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.05)
		tmp = x + y;
	elseif ((1.0 - z) <= 1e+57)
		tmp = t_0;
	elseif ((1.0 - z) <= 5e+207)
		tmp = x * -z;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], 0.98], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.05], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+57], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+207], N[(x * (-z)), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 z) < 0.97999999999999998 or 1.05000000000000004 < (-.f64 1 z) < 1.00000000000000005e57

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 51.5%

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

   if 0.97999999999999998 < (-.f64 1 z) < 1.05000000000000004

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   4. Simplified 98.4%

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

   if 1.00000000000000005e57 < (-.f64 1 z) < 4.9999999999999999e207

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 46.7%

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

      1. *-commutative 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in z around inf 46.7%

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

      1. associate-*r* 46.7%

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

      2. mul-1-neg 46.7%

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

      3. *-commutative 46.7%

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

   7. Simplified 46.7%

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

   if 4.9999999999999999e207 < (-.f64 1 z)

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. *-commutative 57.3%

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

      3. distribute-rgt-neg-out 57.3%

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

   7. Simplified 57.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq 0.98:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 1.05:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+57}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+214}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -11.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+95} \lor \neg \left(z \leq 4.8 \cdot 10^{+141}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))) (t_1 (* x (- z))))
   (if (<= z -2.5e+214)
     t_0
     (if (<= z -2.1e+57)
       t_1
       (if (<= z -11.5)
         t_0
         (if (<= z 1.0)
           (+ x y)
           (if (or (<= z 5.4e+95) (not (<= z 4.8e+141))) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double t_1 = x * -z;
	double tmp;
	if (z <= -2.5e+214) {
		tmp = t_0;
	} else if (z <= -2.1e+57) {
		tmp = t_1;
	} else if (z <= -11.5) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 5.4e+95) || !(z <= 4.8e+141)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = x * -z
    if (z <= (-2.5d+214)) then
        tmp = t_0
    else if (z <= (-2.1d+57)) then
        tmp = t_1
    else if (z <= (-11.5d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 5.4d+95) .or. (.not. (z <= 4.8d+141))) then
        tmp = t_0
    else
        tmp = t_1
    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 = x * -z;
	double tmp;
	if (z <= -2.5e+214) {
		tmp = t_0;
	} else if (z <= -2.1e+57) {
		tmp = t_1;
	} else if (z <= -11.5) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 5.4e+95) || !(z <= 4.8e+141)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	t_1 = x * -z
	tmp = 0
	if z <= -2.5e+214:
		tmp = t_0
	elif z <= -2.1e+57:
		tmp = t_1
	elif z <= -11.5:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 5.4e+95) or not (z <= 4.8e+141):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -2.5e+214)
		tmp = t_0;
	elseif (z <= -2.1e+57)
		tmp = t_1;
	elseif (z <= -11.5)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 5.4e+95) || !(z <= 4.8e+141))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	t_1 = x * -z;
	tmp = 0.0;
	if (z <= -2.5e+214)
		tmp = t_0;
	elseif (z <= -2.1e+57)
		tmp = t_1;
	elseif (z <= -11.5)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 5.4e+95) || ~((z <= 4.8e+141)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.5e+214], t$95$0, If[LessEqual[z, -2.1e+57], t$95$1, If[LessEqual[z, -11.5], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 5.4e+95], N[Not[LessEqual[z, 4.8e+141]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999977e214 or -2.09999999999999991e57 < z < -11.5 or 1 < z < 5.4e95 or 4.79999999999999995e141 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.0%

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

      1. associate-*r* 99.0%

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

      2. neg-mul-1 99.0%

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

      3. *-commutative 99.0%

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

      4. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   5. Taylor expanded in y around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. *-commutative 51.0%

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

      3. distribute-rgt-neg-out 51.0%

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

   7. Simplified 51.0%

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

   if -2.49999999999999977e214 < z < -2.09999999999999991e57 or 5.4e95 < z < 4.79999999999999995e141

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 44.5%

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

      1. *-commutative 44.5%

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

   4. Simplified 44.5%

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

   5. Taylor expanded in z around inf 44.5%

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

      1. associate-*r* 44.5%

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

      2. mul-1-neg 44.5%

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

      3. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   if -11.5 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.2%

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

      1. +-commutative 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -11.5:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+95} \lor \neg \left(z \leq 4.8 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -40000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -40000000000000.0) (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) <= -40000000000000.0) || !((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) <= (-40000000000000.0d0)) .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) <= -40000000000000.0) || !((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) <= -40000000000000.0) 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) <= -40000000000000.0) || !(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) <= -40000000000000.0) || ~(((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], -40000000000000.0], 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 1 z) < -4e13 or 2 < (-.f64 1 z)

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.3%

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

      1. associate-*r* 99.3%

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

      2. neg-mul-1 99.3%

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

      3. *-commutative 99.3%

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

      4. +-commutative 99.3%

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

   4. Simplified 99.3%

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

   if -4e13 < (-.f64 1 z) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.2%

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

      1. +-commutative 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -40000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+25} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.2e+25) (not (<= z 1.0))) (* x (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e+25) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-6.2d+25)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e+25) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.2e+25) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.2e+25) || !(z <= 1.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.2e+25) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.2e+25], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999996e25 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 49.1%

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

      1. *-commutative 49.1%

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

   4. Simplified 49.1%

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

   5. Taylor expanded in z around inf 49.0%

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

      1. associate-*r* 49.0%

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

      2. mul-1-neg 49.0%

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

      3. *-commutative 49.0%

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

   7. Simplified 49.0%

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

   if -6.1999999999999996e25 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

   4. Simplified 93.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+25} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.1e-125) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.1e-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 <= 2.1d-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 <= 2.1e-125) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.1e-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 <= 2.1e-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 <= 2.1e-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, 2.1e-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 < 2.1e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 56.7%

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

      1. *-commutative 56.7%

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

   4. Simplified 56.7%

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

   if 2.1e-125 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-125}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5e-125) (- x (* x z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5e-125) {
		tmp = x - (x * 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 <= 2.5d-125) then
        tmp = x - (x * 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 <= 2.5e-125) {
		tmp = x - (x * z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5e-125:
		tmp = x - (x * z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5e-125)
		tmp = Float64(x - Float64(x * 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 <= 2.5e-125)
		tmp = x - (x * z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5e-125], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.49999999999999983e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 56.7%

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

      1. *-commutative 56.7%

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

   4. Simplified 56.7%

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

   5. Taylor expanded in z around 0 56.7%

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

      1. associate-*r* 56.7%

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

      2. mul-1-neg 56.7%

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

      3. *-commutative 56.7%

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

   7. Simplified 56.7%

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

      1. distribute-rgt-neg-out 56.7%

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

      2. unsub-neg 56.7%

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

      3. *-commutative 56.7%

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

   9. Applied egg-rr 56.7%

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

   if 2.49999999999999983e-125 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-125}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8: 31.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -4.4e-129) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e-129) {
		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 (x <= (-4.4d-129)) 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 (x <= -4.4e-129) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e-129:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e-129)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e-129)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e-129], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -4.40000000000000006e-129

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.5%

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

      1. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in z around 0 34.1%

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

   if -4.40000000000000006e-129 < x

   1. Initial program 100.0%

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

      1. flip3-+ 35.8%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {y}^{3}}{x \cdot x + \left(y \cdot y - x \cdot y\right)}} \cdot \left(1 - z\right) \]

      2. clear-num 35.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(y \cdot y - x \cdot y\right)}{{x}^{3} + {y}^{3}}}} \cdot \left(1 - z\right) \]

      3. associate-*l/ 35.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(1 - z\right)}{\frac{x \cdot x + \left(y \cdot y - x \cdot y\right)}{{x}^{3} + {y}^{3}}}} \]

      4. *-un-lft-identity 35.7%

         \[\leadsto \frac{\color{blue}{1 - z}}{\frac{x \cdot x + \left(y \cdot y - x \cdot y\right)}{{x}^{3} + {y}^{3}}} \]

      5. *-un-lft-identity 35.7%

         \[\leadsto \frac{1 - z}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(y \cdot y - x \cdot y\right)\right)}}{{x}^{3} + {y}^{3}}} \]

      6. associate-/l* 35.7%

         \[\leadsto \frac{1 - z}{\color{blue}{\frac{1}{\frac{{x}^{3} + {y}^{3}}{x \cdot x + \left(y \cdot y - x \cdot y\right)}}}} \]

      7. flip3-+ 99.8%

         \[\leadsto \frac{1 - z}{\frac{1}{\color{blue}{x + y}}} \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{1 - z}{\frac{1}{x + y}}} \]

   4. Taylor expanded in x around 0 59.5%

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

   5. Taylor expanded in z around 0 27.7%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 50.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x y))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + y
end function

Java

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

Python

def code(x, y, z):
	return x + y

Julia

function code(x, y, z)
	return Float64(x + y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + y;
end

Wolfram

code[x_, y_, z_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in z around 0 47.1%

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

   1. +-commutative 47.1%

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

4. Simplified 47.1%

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

5. Final simplification 47.1%

   \[\leadsto x + y \]

Alternative 10: 25.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf 48.4%

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

   1. *-commutative 48.4%

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

4. Simplified 48.4%

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

5. Taylor expanded in z around 0 23.1%

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

6. Final simplification 23.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023305 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))