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

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 7

Speedup: 1.0×

• 21.6% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return (1.0 - z) * (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 = (1.0d0 - z) * (y + x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ t_1 := \left(-z\right) \cdot y\\ \mathbf{if}\;1 - z \leq -1 \cdot 10^{+157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq -20:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)) (t_1 (* (- z) y)))
   (if (<= (- 1.0 z) -1e+157)
     t_0
     (if (<= (- 1.0 z) -20.0)
       t_1
       (if (<= (- 1.0 z) 2.0) (+ y x) (if (<= (- 1.0 z) 1e+126) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = -z * x;
	double t_1 = -z * y;
	double tmp;
	if ((1.0 - z) <= -1e+157) {
		tmp = t_0;
	} else if ((1.0 - z) <= -20.0) {
		tmp = t_1;
	} else if ((1.0 - z) <= 2.0) {
		tmp = y + x;
	} else if ((1.0 - z) <= 1e+126) {
		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 = -z * x
    t_1 = -z * y
    if ((1.0d0 - z) <= (-1d+157)) then
        tmp = t_0
    else if ((1.0d0 - z) <= (-20.0d0)) then
        tmp = t_1
    else if ((1.0d0 - z) <= 2.0d0) then
        tmp = y + x
    else if ((1.0d0 - z) <= 1d+126) 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 = -z * x;
	double t_1 = -z * y;
	double tmp;
	if ((1.0 - z) <= -1e+157) {
		tmp = t_0;
	} else if ((1.0 - z) <= -20.0) {
		tmp = t_1;
	} else if ((1.0 - z) <= 2.0) {
		tmp = y + x;
	} else if ((1.0 - z) <= 1e+126) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * x
	t_1 = -z * y
	tmp = 0
	if (1.0 - z) <= -1e+157:
		tmp = t_0
	elif (1.0 - z) <= -20.0:
		tmp = t_1
	elif (1.0 - z) <= 2.0:
		tmp = y + x
	elif (1.0 - z) <= 1e+126:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * x)
	t_1 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (Float64(1.0 - z) <= -1e+157)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= -20.0)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(y + x);
	elseif (Float64(1.0 - z) <= 1e+126)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z * x;
	t_1 = -z * y;
	tmp = 0.0;
	if ((1.0 - z) <= -1e+157)
		tmp = t_0;
	elseif ((1.0 - z) <= -20.0)
		tmp = t_1;
	elseif ((1.0 - z) <= 2.0)
		tmp = y + x;
	elseif ((1.0 - z) <= 1e+126)
		tmp = t_0;
	else
		tmp = t_1;
	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[N[(1.0 - z), $MachinePrecision], -1e+157], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], -20.0], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(y + x), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+126], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -9.99999999999999983e156 or 2 < (-.f64 #s(literal 1 binary64) z) < 9.99999999999999925e125

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   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 66.9

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 65.7%

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

   if -9.99999999999999983e156 < (-.f64 #s(literal 1 binary64) z) < -20 or 9.99999999999999925e125 < (-.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 y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
   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 63.9

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

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 62.1%

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

   if -20 < (-.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

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

      1. +-commutative N/A

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

      2. lower-+.f64 99.0

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

   5. Applied rewrites 99.0%

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

Alternative 3: 40.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-203}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;y + x \leq 10^{-67}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y + x \leq 5 \cdot 10^{+135}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ y x) -5e-203)
   (* (- 1.0 z) x)
   (if (<= (+ y x) 1e-67)
     (+ y x)
     (if (<= (+ y x) 5e+135) (* (- z) y) (* 1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y + x) <= -5e-203) {
		tmp = (1.0 - z) * x;
	} else if ((y + x) <= 1e-67) {
		tmp = y + x;
	} else if ((y + x) <= 5e+135) {
		tmp = -z * y;
	} else {
		tmp = 1.0 * 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 ((y + x) <= (-5d-203)) then
        tmp = (1.0d0 - z) * x
    else if ((y + x) <= 1d-67) then
        tmp = y + x
    else if ((y + x) <= 5d+135) then
        tmp = -z * y
    else
        tmp = 1.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y + x) <= -5e-203) {
		tmp = (1.0 - z) * x;
	} else if ((y + x) <= 1e-67) {
		tmp = y + x;
	} else if ((y + x) <= 5e+135) {
		tmp = -z * y;
	} else {
		tmp = 1.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y + x) <= -5e-203:
		tmp = (1.0 - z) * x
	elif (y + x) <= 1e-67:
		tmp = y + x
	elif (y + x) <= 5e+135:
		tmp = -z * y
	else:
		tmp = 1.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y + x) <= -5e-203)
		tmp = Float64(Float64(1.0 - z) * x);
	elseif (Float64(y + x) <= 1e-67)
		tmp = Float64(y + x);
	elseif (Float64(y + x) <= 5e+135)
		tmp = Float64(Float64(-z) * y);
	else
		tmp = Float64(1.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y + x) <= -5e-203)
		tmp = (1.0 - z) * x;
	elseif ((y + x) <= 1e-67)
		tmp = y + x;
	elseif ((y + x) <= 5e+135)
		tmp = -z * y;
	else
		tmp = 1.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y + x), $MachinePrecision], -5e-203], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(y + x), $MachinePrecision], 1e-67], N[(y + x), $MachinePrecision], If[LessEqual[N[(y + x), $MachinePrecision], 5e+135], N[((-z) * y), $MachinePrecision], N[(1.0 * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x y) < -5.0000000000000002e-203

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   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 51.2

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

   5. Applied rewrites 51.2%

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

   if -5.0000000000000002e-203 < (+.f64 x y) < 9.99999999999999943e-68

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if 9.99999999999999943e-68 < (+.f64 x y) < 5.00000000000000029e135

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
   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 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 44.4%

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

   if 5.00000000000000029e135 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
   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 46.4

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

   5. Applied rewrites 46.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 31.3%

      \[\leadsto 1 \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-203}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;y + x \leq 10^{-67}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y + x \leq 5 \cdot 10^{+135}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot \left(y + x\right)\\ \mathbf{if}\;1 - z \leq -20:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) (+ y x))))
   (if (<= (- 1.0 z) -20.0) t_0 (if (<= (- 1.0 z) 2.0) (+ y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z * (y + x);
	double tmp;
	if ((1.0 - z) <= -20.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		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 * (y + x)
    if ((1.0d0 - z) <= (-20.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) 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 * (y + x);
	double tmp;
	if ((1.0 - z) <= -20.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * (y + x)
	tmp = 0
	if (1.0 - z) <= -20.0:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * Float64(y + x))
	tmp = 0.0
	if (Float64(1.0 - z) <= -20.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z * (y + x);
	tmp = 0.0;
	if ((1.0 - z) <= -20.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -20.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -20 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 97.0

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

   5. Applied rewrites 97.0%

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

   if -20 < (-.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

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

      1. +-commutative N/A

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

      2. lower-+.f64 99.0

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

   5. Applied rewrites 99.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -20:\\ \;\;\;\;\left(-z\right) \cdot \left(y + x\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ \mathbf{if}\;1 - z \leq -20:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)))
   (if (<= (- 1.0 z) -20.0) t_0 (if (<= (- 1.0 z) 2.0) (+ y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if ((1.0 - z) <= -20.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		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 ((1.0d0 - z) <= (-20.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) 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 ((1.0 - z) <= -20.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * x
	tmp = 0
	if (1.0 - z) <= -20.0:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		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 (Float64(1.0 - z) <= -20.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		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 ((1.0 - z) <= -20.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		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[N[(1.0 - z), $MachinePrecision], -20.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -20 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 y around 0

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   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 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 50.4%

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

   if -20 < (-.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

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

      1. +-commutative N/A

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

      2. lower-+.f64 99.0

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

   5. Applied rewrites 99.0%

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

Alternative 6: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-260}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ y x) -5e-260) (* (- 1.0 z) x) (* (- 1.0 z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y + x) <= -5e-260) {
		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 ((y + x) <= (-5d-260)) 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 ((y + x) <= -5e-260) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (1.0 - z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y + x) <= -5e-260:
		tmp = (1.0 - z) * x
	else:
		tmp = (1.0 - z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y + x) <= -5e-260)
		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 ((y + x) <= -5e-260)
		tmp = (1.0 - z) * x;
	else
		tmp = (1.0 - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y + x), $MachinePrecision], -5e-260], 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) < -5.0000000000000003e-260

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   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 51.9

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

   5. Applied rewrites 51.9%

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

   if -5.0000000000000003e-260 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
   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 50.9

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

   5. Applied rewrites 50.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-260}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.8% 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 z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 48.9

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

5. Applied rewrites 48.9%

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

Reproduce

herbie shell --seed 2024254 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))