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

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 7

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -21:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+189} \lor \neg \left(z \leq 9.2 \cdot 10^{+252}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -21.0)
     t_0
     (if (<= z 1.0)
       (+ x y)
       (if (or (<= z 3.8e+189) (not (<= z 9.2e+252))) (* y (- z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -21.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 3.8e+189) || !(z <= 9.2e+252)) {
		tmp = y * -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (z <= (-21.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 3.8d+189) .or. (.not. (z <= 9.2d+252))) then
        tmp = y * -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -21.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 3.8e+189) || !(z <= 9.2e+252)) {
		tmp = y * -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -21.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 3.8e+189) or not (z <= 9.2e+252):
		tmp = y * -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -21.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 3.8e+189) || !(z <= 9.2e+252))
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -21.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 3.8e+189) || ~((z <= 9.2e+252)))
		tmp = y * -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -21.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 3.8e+189], N[Not[LessEqual[z, 9.2e+252]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -21 or 3.7999999999999998e189 < z < 9.1999999999999999e252

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-lft-neg-out 98.8%

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

      3. *-commutative 98.8%

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

      4. +-commutative 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in y around 0 54.4%

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

      1. associate-*r* 54.4%

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

      2. mul-1-neg 54.4%

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

   8. Simplified 54.4%

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

   if -21 < 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 99.1%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

   if 1 < z < 3.7999999999999998e189 or 9.1999999999999999e252 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-lft-neg-out 98.4%

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

      3. *-commutative 98.4%

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

      4. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. fma-define 84.2%

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

      3. mul-1-neg 84.2%

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

      4. fma-neg 84.2%

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

      5. *-commutative 84.2%

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

      6. associate-/l* 87.4%

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

      7. distribute-lft-out-- 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in x around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. distribute-rgt-neg-out 57.6%

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

   11. Simplified 57.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -21:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+189} \lor \neg \left(z \leq 9.2 \cdot 10^{+252}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -18.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.14:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+253}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -18.5)
     t_0
     (if (<= z 0.14)
       (+ x y)
       (if (<= z 2.75e+193)
         (* y (- 1.0 z))
         (if (<= z 1.3e+253) t_0 (* y (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -18.5) {
		tmp = t_0;
	} else if (z <= 0.14) {
		tmp = x + y;
	} else if (z <= 2.75e+193) {
		tmp = y * (1.0 - z);
	} else if (z <= 1.3e+253) {
		tmp = t_0;
	} 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 = x * -z
    if (z <= (-18.5d0)) then
        tmp = t_0
    else if (z <= 0.14d0) then
        tmp = x + y
    else if (z <= 2.75d+193) then
        tmp = y * (1.0d0 - z)
    else if (z <= 1.3d+253) then
        tmp = t_0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -18.5) {
		tmp = t_0;
	} else if (z <= 0.14) {
		tmp = x + y;
	} else if (z <= 2.75e+193) {
		tmp = y * (1.0 - z);
	} else if (z <= 1.3e+253) {
		tmp = t_0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -18.5:
		tmp = t_0
	elif z <= 0.14:
		tmp = x + y
	elif z <= 2.75e+193:
		tmp = y * (1.0 - z)
	elif z <= 1.3e+253:
		tmp = t_0
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -18.5)
		tmp = t_0;
	elseif (z <= 0.14)
		tmp = Float64(x + y);
	elseif (z <= 2.75e+193)
		tmp = Float64(y * Float64(1.0 - z));
	elseif (z <= 1.3e+253)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -18.5)
		tmp = t_0;
	elseif (z <= 0.14)
		tmp = x + y;
	elseif (z <= 2.75e+193)
		tmp = y * (1.0 - z);
	elseif (z <= 1.3e+253)
		tmp = t_0;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -18.5], t$95$0, If[LessEqual[z, 0.14], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.75e+193], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+253], t$95$0, N[(y * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -18.5 or 2.7500000000000001e193 < z < 1.3e253

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-lft-neg-out 98.8%

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

      3. *-commutative 98.8%

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

      4. +-commutative 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in y around 0 54.4%

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

      1. associate-*r* 54.4%

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

      2. mul-1-neg 54.4%

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

   8. Simplified 54.4%

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

   if -18.5 < z < 0.14000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.1%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

   if 0.14000000000000001 < z < 2.7500000000000001e193

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 58.3%

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

   if 1.3e253 < 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 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 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%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. fma-define 77.8%

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

      3. mul-1-neg 77.8%

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

      4. fma-neg 77.8%

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

      5. *-commutative 77.8%

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

      6. associate-/l* 85.5%

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

      7. distribute-lft-out-- 85.5%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in x around 0 55.3%

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

       1. mul-1-neg 55.3%

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

       2. distribute-rgt-neg-out 55.3%

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

   11. Simplified 55.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18.5:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 0.14:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-68} \lor \neg \left(y \leq 5.2 \cdot 10^{-13}\right) \land y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 1.75e-68) (and (not (<= y 5.2e-13)) (<= y 5e+19)))
   (* x (- 1.0 z))
   (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.75e-68) || (!(y <= 5.2e-13) && (y <= 5e+19))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= 1.75d-68) .or. (.not. (y <= 5.2d-13)) .and. (y <= 5d+19)) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.75e-68) || (!(y <= 5.2e-13) && (y <= 5e+19))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 1.75e-68) or (not (y <= 5.2e-13) and (y <= 5e+19)):
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 1.75e-68) || (!(y <= 5.2e-13) && (y <= 5e+19)))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 1.75e-68) || (~((y <= 5.2e-13)) && (y <= 5e+19)))
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 1.75e-68], And[N[Not[LessEqual[y, 5.2e-13]], $MachinePrecision], LessEqual[y, 5e+19]]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.75000000000000006e-68 or 5.2000000000000001e-13 < y < 5e19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.2%

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

      1. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if 1.75000000000000006e-68 < y < 5.2000000000000001e-13 or 5e19 < 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 78.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-68} \lor \neg \left(y \leq 5.2 \cdot 10^{-13}\right) \land y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -4000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -4000000.0) (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) <= -4000000.0) || !((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) <= (-4000000.0d0)) .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) <= -4000000.0) || !((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) <= -4000000.0) 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) <= -4000000.0) || !(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) <= -4000000.0) || ~(((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], -4000000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -4e6 or 2 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. distribute-lft-neg-out 98.6%

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

      3. *-commutative 98.6%

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

      4. +-commutative 98.6%

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

   5. Simplified 98.6%

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

   if -4e6 < (-.f64 #s(literal 1 binary64) z) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.1%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -4000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -128000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -128000000000.0) (not (<= z 1.0))) (* y (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -128000000000.0) || !(z <= 1.0)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-128000000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = y * -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -128000000000.0) || !(z <= 1.0)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -128000000000.0) or not (z <= 1.0):
		tmp = y * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -128000000000.0) || !(z <= 1.0))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -128000000000.0) || ~((z <= 1.0)))
		tmp = y * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -128000000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e11 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. distribute-lft-neg-out 99.2%

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

      3. *-commutative 99.2%

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

      4. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x around inf 82.6%

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

      1. *-commutative 82.6%

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

      2. fma-define 82.6%

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

      3. mul-1-neg 82.6%

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

      4. fma-neg 82.6%

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

      5. *-commutative 82.6%

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

      6. associate-/l* 86.7%

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

      7. distribute-lft-out-- 86.7%

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

   8. Simplified 86.7%

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

   9. Taylor expanded in x around 0 52.1%

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

       1. mul-1-neg 52.1%

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

       2. distribute-rgt-neg-out 52.1%

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

   11. Simplified 52.1%

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

   if -1.28e11 < 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 2 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -128000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.3% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0 44.9%

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

   1. +-commutative 44.9%

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

5. Simplified 44.9%

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

6. Final simplification 44.9%

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

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))