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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

Speedup: 1.0×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 75.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ t_1 := z \cdot \left(-y\right)\\ t_2 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;1 - z \leq 0.8:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 10^{+150} \lor \neg \left(1 - z \leq 10^{+175}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))) (t_1 (* z (- y))) (t_2 (* z (- x))))
   (if (<= (- 1.0 z) -5e+82)
     t_1
     (if (<= (- 1.0 z) -2e+46)
       t_2
       (if (<= (- 1.0 z) 0.8)
         t_0
         (if (<= (- 1.0 z) 2.0)
           (+ x y)
           (if (<= (- 1.0 z) 1e+45)
             t_0
             (if (or (<= (- 1.0 z) 1e+150) (not (<= (- 1.0 z) 1e+175)))
               t_2
               t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double t_1 = z * -y;
	double t_2 = z * -x;
	double tmp;
	if ((1.0 - z) <= -5e+82) {
		tmp = t_1;
	} else if ((1.0 - z) <= -2e+46) {
		tmp = t_2;
	} else if ((1.0 - z) <= 0.8) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 1e+45) {
		tmp = t_0;
	} else if (((1.0 - z) <= 1e+150) || !((1.0 - z) <= 1e+175)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    t_1 = z * -y
    t_2 = z * -x
    if ((1.0d0 - z) <= (-5d+82)) then
        tmp = t_1
    else if ((1.0d0 - z) <= (-2d+46)) then
        tmp = t_2
    else if ((1.0d0 - z) <= 0.8d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) then
        tmp = x + y
    else if ((1.0d0 - z) <= 1d+45) then
        tmp = t_0
    else if (((1.0d0 - z) <= 1d+150) .or. (.not. ((1.0d0 - z) <= 1d+175))) then
        tmp = t_2
    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 * (1.0 - z);
	double t_1 = z * -y;
	double t_2 = z * -x;
	double tmp;
	if ((1.0 - z) <= -5e+82) {
		tmp = t_1;
	} else if ((1.0 - z) <= -2e+46) {
		tmp = t_2;
	} else if ((1.0 - z) <= 0.8) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 1e+45) {
		tmp = t_0;
	} else if (((1.0 - z) <= 1e+150) || !((1.0 - z) <= 1e+175)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	t_1 = z * -y
	t_2 = z * -x
	tmp = 0
	if (1.0 - z) <= -5e+82:
		tmp = t_1
	elif (1.0 - z) <= -2e+46:
		tmp = t_2
	elif (1.0 - z) <= 0.8:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		tmp = x + y
	elif (1.0 - z) <= 1e+45:
		tmp = t_0
	elif ((1.0 - z) <= 1e+150) or not ((1.0 - z) <= 1e+175):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	t_1 = Float64(z * Float64(-y))
	t_2 = Float64(z * Float64(-x))
	tmp = 0.0
	if (Float64(1.0 - z) <= -5e+82)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= -2e+46)
		tmp = t_2;
	elseif (Float64(1.0 - z) <= 0.8)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(x + y);
	elseif (Float64(1.0 - z) <= 1e+45)
		tmp = t_0;
	elseif ((Float64(1.0 - z) <= 1e+150) || !(Float64(1.0 - z) <= 1e+175))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	t_1 = z * -y;
	t_2 = z * -x;
	tmp = 0.0;
	if ((1.0 - z) <= -5e+82)
		tmp = t_1;
	elseif ((1.0 - z) <= -2e+46)
		tmp = t_2;
	elseif ((1.0 - z) <= 0.8)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		tmp = x + y;
	elseif ((1.0 - z) <= 1e+45)
		tmp = t_0;
	elseif (((1.0 - z) <= 1e+150) || ~(((1.0 - z) <= 1e+175)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+82], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], -2e+46], t$95$2, If[LessEqual[N[(1.0 - z), $MachinePrecision], 0.8], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+45], t$95$0, If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+150], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+175]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 z) < -5.00000000000000015e82 or 9.99999999999999981e149 < (-.f64 1 z) < 9.9999999999999994e174

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 55.6%

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

   3. Taylor expanded in z around inf 55.6%

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

      1. associate-*r* 55.6%

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

      2. mul-1-neg 55.6%

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

   5. Simplified 55.6%

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

   if -5.00000000000000015e82 < (-.f64 1 z) < -2e46 or 9.9999999999999993e44 < (-.f64 1 z) < 9.99999999999999981e149 or 9.9999999999999994e174 < (-.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%

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

      1. mul-1-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt-neg-out 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 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. *-commutative 59.2%

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

      3. distribute-rgt-neg-in 59.2%

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

   7. Simplified 59.2%

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

   if -2e46 < (-.f64 1 z) < 0.80000000000000004 or 2 < (-.f64 1 z) < 9.9999999999999993e44

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 41.2%

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

   if 0.80000000000000004 < (-.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%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 0.8:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+45}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 10^{+150} \lor \neg \left(1 - z \leq 10^{+175}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -48000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+34} \lor \neg \left(z \leq 6.6 \cdot 10^{+79}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* z (- y))))
   (if (<= z -1.06e+175)
     t_0
     (if (<= z -3.05e+156)
       t_1
       (if (<= z -48000.0)
         t_0
         (if (<= z 1.0)
           (+ x y)
           (if (or (<= z 7.4e+34) (not (<= z 6.6e+79))) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = z * -y;
	double tmp;
	if (z <= -1.06e+175) {
		tmp = t_0;
	} else if (z <= -3.05e+156) {
		tmp = t_1;
	} else if (z <= -48000.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 7.4e+34) || !(z <= 6.6e+79)) {
		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 = z * -x
    t_1 = z * -y
    if (z <= (-1.06d+175)) then
        tmp = t_0
    else if (z <= (-3.05d+156)) then
        tmp = t_1
    else if (z <= (-48000.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 7.4d+34) .or. (.not. (z <= 6.6d+79))) 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 = z * -x;
	double t_1 = z * -y;
	double tmp;
	if (z <= -1.06e+175) {
		tmp = t_0;
	} else if (z <= -3.05e+156) {
		tmp = t_1;
	} else if (z <= -48000.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 7.4e+34) || !(z <= 6.6e+79)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = z * -y
	tmp = 0
	if z <= -1.06e+175:
		tmp = t_0
	elif z <= -3.05e+156:
		tmp = t_1
	elif z <= -48000.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 7.4e+34) or not (z <= 6.6e+79):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (z <= -1.06e+175)
		tmp = t_0;
	elseif (z <= -3.05e+156)
		tmp = t_1;
	elseif (z <= -48000.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 7.4e+34) || !(z <= 6.6e+79))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = z * -y;
	tmp = 0.0;
	if (z <= -1.06e+175)
		tmp = t_0;
	elseif (z <= -3.05e+156)
		tmp = t_1;
	elseif (z <= -48000.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 7.4e+34) || ~((z <= 6.6e+79)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[z, -1.06e+175], t$95$0, If[LessEqual[z, -3.05e+156], t$95$1, If[LessEqual[z, -48000.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 7.4e+34], N[Not[LessEqual[z, 6.6e+79]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06e175 or -3.0500000000000001e156 < z < -48000 or 7.40000000000000017e34 < z < 6.6000000000000003e79

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. distribute-rgt-neg-out 99.4%

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

      4. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in y around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

   7. Simplified 58.5%

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

   if -1.06e175 < z < -3.0500000000000001e156 or 1 < z < 7.40000000000000017e34 or 6.6000000000000003e79 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 52.9%

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

   3. Taylor expanded in z around inf 52.8%

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

      1. associate-*r* 52.8%

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

      2. mul-1-neg 52.8%

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

   5. Simplified 52.8%

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

   if -48000 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.7%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+175}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -48000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+34} \lor \neg \left(z \leq 6.6 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -5000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -5000000000000.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- y) x))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -5000000000000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - z) <= (-5000000000000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-y - x)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -5000000000000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -5000000000000.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-y - x)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -5000000000000.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-y) - x));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -5000000000000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-y - x);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -5000000000000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -5e12 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 99.0%

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

      1. mul-1-neg 99.0%

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

      2. +-commutative 99.0%

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

      3. distribute-rgt-neg-out 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%

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

   if -5e12 < (-.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 96.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-59} \lor \neg \left(x \leq -1.15 \cdot 10^{-88}\right) \land x \leq -2.3 \cdot 10^{-117}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-59) (and (not (<= x -1.15e-88)) (<= x -2.3e-117)))
   (- x (* x z))
   (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-59) || (!(x <= -1.15e-88) && (x <= -2.3e-117))) {
		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 ((x <= (-2.1d-59)) .or. (.not. (x <= (-1.15d-88))) .and. (x <= (-2.3d-117))) 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 ((x <= -2.1e-59) || (!(x <= -1.15e-88) && (x <= -2.3e-117))) {
		tmp = x - (x * z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-59) or (not (x <= -1.15e-88) and (x <= -2.3e-117)):
		tmp = x - (x * z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-59) || (!(x <= -1.15e-88) && (x <= -2.3e-117)))
		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 ((x <= -2.1e-59) || (~((x <= -1.15e-88)) && (x <= -2.3e-117)))
		tmp = x - (x * z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-59], And[N[Not[LessEqual[x, -1.15e-88]], $MachinePrecision], LessEqual[x, -2.3e-117]]], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999997e-59 or -1.14999999999999993e-88 < x < -2.29999999999999994e-117

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 77.0%

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

      1. sub-neg 77.0%

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

      2. +-commutative 77.0%

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

      3. distribute-rgt1-in 77.0%

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

      4. distribute-lft-neg-out 77.0%

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

      5. unsub-neg 77.0%

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

   4. Simplified 77.0%

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

   if -2.09999999999999997e-59 < x < -1.14999999999999993e-88 or -2.29999999999999994e-117 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 62.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-59} \lor \neg \left(x \leq -1.15 \cdot 10^{-88}\right) \land x \leq -2.3 \cdot 10^{-117}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 6: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -48000.0) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000.0) || !(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 <= (-48000.0d0)) .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 <= -48000.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -48000.0) 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 <= -48000.0) || !(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 <= -48000.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -48000.0], 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 < -48000 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. distribute-rgt-neg-out 99.4%

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

      4. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in y around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. *-commutative 54.9%

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

      3. distribute-rgt-neg-in 54.9%

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

   7. Simplified 54.9%

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

   if -48000 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 51.2% 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 41.5%

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

3. Final simplification 41.5%

   \[\leadsto x + y \]

Alternative 8: 26.2% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 50.6%

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

3. Taylor expanded in z around 0 22.4%

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

4. Final simplification 22.4%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))