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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. distribute-lft-in N/A

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

   6. *-rgt-identity N/A

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

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(x + y, \mathsf{neg}\left(z\right), x + y\right)} \]

   8. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{x + y}, \mathsf{neg}\left(z\right), x + y\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{y + x}, \mathsf{neg}\left(z\right), x + y\right) \]

   10. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y + x}, \mathsf{neg}\left(z\right), x + y\right) \]

   11. lower-neg.f64 100.0

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

   12. lift-+.f64 N/A

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

   13. +-commutative N/A

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

   14. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + x, -z, y + x\right)} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq 0.9999999999999:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;1 - z \leq 100:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+171}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 z) 0.9999999999999)
   (* (- 1.0 z) x)
   (if (<= (- 1.0 z) 100.0)
     (+ y x)
     (if (<= (- 1.0 z) 2e+171) (* (- y) z) (* (- z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - z) <= 0.9999999999999) {
		tmp = (1.0 - z) * x;
	} else if ((1.0 - z) <= 100.0) {
		tmp = y + x;
	} else if ((1.0 - z) <= 2e+171) {
		tmp = -y * z;
	} else {
		tmp = -z * x;
	}
	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) <= 0.9999999999999d0) then
        tmp = (1.0d0 - z) * x
    else if ((1.0d0 - z) <= 100.0d0) then
        tmp = y + x
    else if ((1.0d0 - z) <= 2d+171) then
        tmp = -y * z
    else
        tmp = -z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - z) <= 0.9999999999999) {
		tmp = (1.0 - z) * x;
	} else if ((1.0 - z) <= 100.0) {
		tmp = y + x;
	} else if ((1.0 - z) <= 2e+171) {
		tmp = -y * z;
	} else {
		tmp = -z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - z) <= 0.9999999999999:
		tmp = (1.0 - z) * x
	elif (1.0 - z) <= 100.0:
		tmp = y + x
	elif (1.0 - z) <= 2e+171:
		tmp = -y * z
	else:
		tmp = -z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - z) <= 0.9999999999999)
		tmp = Float64(Float64(1.0 - z) * x);
	elseif (Float64(1.0 - z) <= 100.0)
		tmp = Float64(y + x);
	elseif (Float64(1.0 - z) <= 2e+171)
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(Float64(-z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - z) <= 0.9999999999999)
		tmp = (1.0 - z) * x;
	elseif ((1.0 - z) <= 100.0)
		tmp = y + x;
	elseif ((1.0 - z) <= 2e+171)
		tmp = -y * z;
	else
		tmp = -z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - z), $MachinePrecision], 0.9999999999999], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 100.0], N[(y + x), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+171], N[((-y) * z), $MachinePrecision], N[((-z) * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 #s(literal 1 binary64) z) < 0.999999999999899969

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.3

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

   5. Applied rewrites 55.3%

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

   if 0.999999999999899969 < (-.f64 #s(literal 1 binary64) z) < 100

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 46.1

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

   5. Applied rewrites 46.1%

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

   7. Applied rewrites 46.1%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 98.9

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

   10. Applied rewrites 98.9%

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

   if 100 < (-.f64 #s(literal 1 binary64) z) < 1.99999999999999991e171

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.8

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 59.0%

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

   if 1.99999999999999991e171 < (-.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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.5%

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

Alternative 3: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+172}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -105:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)))
   (if (<= z -1.8e+172)
     t_0
     (if (<= z -105.0) (* (- y) z) (if (<= z 1.0) (+ y x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if (z <= -1.8e+172) {
		tmp = t_0;
	} else if (z <= -105.0) {
		tmp = -y * z;
	} else if (z <= 1.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z * x
    if (z <= (-1.8d+172)) then
        tmp = t_0
    else if (z <= (-105.0d0)) then
        tmp = -y * z
    else if (z <= 1.0d0) then
        tmp = y + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if (z <= -1.8e+172) {
		tmp = t_0;
	} else if (z <= -105.0) {
		tmp = -y * z;
	} else if (z <= 1.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * x
	tmp = 0
	if z <= -1.8e+172:
		tmp = t_0
	elif z <= -105.0:
		tmp = -y * z
	elif z <= 1.0:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * x)
	tmp = 0.0
	if (z <= -1.8e+172)
		tmp = t_0;
	elseif (z <= -105.0)
		tmp = Float64(Float64(-y) * z);
	elseif (z <= 1.0)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z * x;
	tmp = 0.0;
	if (z <= -1.8e+172)
		tmp = t_0;
	elseif (z <= -105.0)
		tmp = -y * z;
	elseif (z <= 1.0)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * x), $MachinePrecision]}, If[LessEqual[z, -1.8e+172], t$95$0, If[LessEqual[z, -105.0], N[((-y) * z), $MachinePrecision], If[LessEqual[z, 1.0], N[(y + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999987e172 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.3%

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

   if -1.79999999999999987e172 < z < -105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.8

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 59.0%

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

   if -105 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.9

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

   5. Applied rewrites 45.9%

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

   7. Applied rewrites 45.9%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 98.2

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

   10. Applied rewrites 98.2%

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

Alternative 4: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -20000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -20000.0) (not (<= (- 1.0 z) 2.0)))
   (* (- z) x)
   (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -20000.0) || !((1.0 - z) <= 2.0)) {
		tmp = -z * x;
	} else {
		tmp = y + x;
	}
	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) <= (-20000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = -z * x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -20000.0) || !((1.0 - z) <= 2.0)) {
		tmp = -z * x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -20000.0) or not ((1.0 - z) <= 2.0):
		tmp = -z * x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -20000.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(Float64(-z) * x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -20000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = -z * x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -20000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[((-z) * x), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -2e4 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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.1

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

   5. Applied rewrites 53.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.8%

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

   if -2e4 < (-.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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.4

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

   5. Applied rewrites 45.4%

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

   7. Applied rewrites 45.5%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 98.8

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

   10. Applied rewrites 98.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -20000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-251}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-251) (fma (- z) x x) (* (- 1.0 z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-251) {
		tmp = fma(-z, x, x);
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-251)
		tmp = fma(Float64(-z), x, x);
	else
		tmp = Float64(Float64(1.0 - z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-251], N[((-z) * x + x), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000002e-251

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.7

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

   5. Applied rewrites 52.7%

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

   7. Applied rewrites 52.7%

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

   if -1.00000000000000002e-251 < (+.f64 x 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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 59.6

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

   5. Applied rewrites 59.6%

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

Alternative 6: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-251}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-251) (* (- 1.0 z) x) (* (- 1.0 z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-251) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * 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 + y) <= (-1d-251)) then
        tmp = (1.0d0 - z) * x
    else
        tmp = (1.0d0 - z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-251) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-251:
		tmp = (1.0 - z) * x
	else:
		tmp = (1.0 - z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-251)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(Float64(1.0 - z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-251)
		tmp = (1.0 - z) * x;
	else
		tmp = (1.0 - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-251], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000002e-251

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.7

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

   5. Applied rewrites 52.7%

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

   if -1.00000000000000002e-251 < (+.f64 x 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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 59.6

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

   5. Applied rewrites 59.6%

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

Alternative 7: 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]

Derivation

1. Initial program 100.0%

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

Alternative 8: 49.7% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 49.3

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

5. Applied rewrites 49.3%

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

7. Applied rewrites 49.3%

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

8. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 50.9

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

10. Applied rewrites 50.9%

    \[\leadsto \color{blue}{y + x} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024324 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))