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

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

Alternatives: 9

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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) * (z + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (z + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 49.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 880000 \lor \neg \left(z \leq 9.8 \cdot 10^{+70}\right) \land z \leq 1.45 \cdot 10^{+135}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e+96)
   (* y z)
   (if (<= z -7.2e+64)
     (* x z)
     (if (<= z -1.0)
       (* y z)
       (if (<= z 2.5e-241)
         x
         (if (<= z 1.1e-53)
           y
           (if (<= z 0.55)
             x
             (if (or (<= z 880000.0)
                     (and (not (<= z 9.8e+70)) (<= z 1.45e+135)))
               (* y z)
               (* x z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+96) {
		tmp = y * z;
	} else if (z <= -7.2e+64) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 2.5e-241) {
		tmp = x;
	} else if (z <= 1.1e-53) {
		tmp = y;
	} else if (z <= 0.55) {
		tmp = x;
	} else if ((z <= 880000.0) || (!(z <= 9.8e+70) && (z <= 1.45e+135))) {
		tmp = y * z;
	} else {
		tmp = x * 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 (z <= (-5.6d+96)) then
        tmp = y * z
    else if (z <= (-7.2d+64)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 2.5d-241) then
        tmp = x
    else if (z <= 1.1d-53) then
        tmp = y
    else if (z <= 0.55d0) then
        tmp = x
    else if ((z <= 880000.0d0) .or. (.not. (z <= 9.8d+70)) .and. (z <= 1.45d+135)) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+96) {
		tmp = y * z;
	} else if (z <= -7.2e+64) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 2.5e-241) {
		tmp = x;
	} else if (z <= 1.1e-53) {
		tmp = y;
	} else if (z <= 0.55) {
		tmp = x;
	} else if ((z <= 880000.0) || (!(z <= 9.8e+70) && (z <= 1.45e+135))) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e+96:
		tmp = y * z
	elif z <= -7.2e+64:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 2.5e-241:
		tmp = x
	elif z <= 1.1e-53:
		tmp = y
	elif z <= 0.55:
		tmp = x
	elif (z <= 880000.0) or (not (z <= 9.8e+70) and (z <= 1.45e+135)):
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e+96)
		tmp = Float64(y * z);
	elseif (z <= -7.2e+64)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 2.5e-241)
		tmp = x;
	elseif (z <= 1.1e-53)
		tmp = y;
	elseif (z <= 0.55)
		tmp = x;
	elseif ((z <= 880000.0) || (!(z <= 9.8e+70) && (z <= 1.45e+135)))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e+96)
		tmp = y * z;
	elseif (z <= -7.2e+64)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 2.5e-241)
		tmp = x;
	elseif (z <= 1.1e-53)
		tmp = y;
	elseif (z <= 0.55)
		tmp = x;
	elseif ((z <= 880000.0) || (~((z <= 9.8e+70)) && (z <= 1.45e+135)))
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e+96], N[(y * z), $MachinePrecision], If[LessEqual[z, -7.2e+64], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.5e-241], x, If[LessEqual[z, 1.1e-53], y, If[LessEqual[z, 0.55], x, If[Or[LessEqual[z, 880000.0], And[N[Not[LessEqual[z, 9.8e+70]], $MachinePrecision], LessEqual[z, 1.45e+135]]], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.59999999999999999e96 or -7.20000000000000027e64 < z < -1 or 0.55000000000000004 < z < 8.8e5 or 9.80000000000000056e70 < z < 1.4499999999999999e135

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 86.0%

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

   4. Taylor expanded in z around inf 85.2%

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

   5. Taylor expanded in y around inf 46.6%

      \[\leadsto \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 46.6%

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

   7. Simplified 46.6%

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

   if -5.59999999999999999e96 < z < -7.20000000000000027e64 or 8.8e5 < z < 9.80000000000000056e70 or 1.4499999999999999e135 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.7%

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

      1. +-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x around inf 83.9%

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

   7. Taylor expanded in x around inf 60.4%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 60.4%

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

   9. Simplified 60.4%

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

   if -1 < z < 2.4999999999999999e-241 or 1.10000000000000009e-53 < z < 0.55000000000000004

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 50.1%

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

      1. +-commutative 50.1%

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

   7. Simplified 50.1%

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

   8. Taylor expanded in z around 0 46.7%

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

   if 2.4999999999999999e-241 < z < 1.10000000000000009e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.4%

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

   4. Taylor expanded in z around 0 54.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 880000 \lor \neg \left(z \leq 9.8 \cdot 10^{+70}\right) \land z \leq 1.45 \cdot 10^{+135}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -4:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+70} \lor \neg \left(z + 1 \leq 2 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -5e+97)
   (* y z)
   (if (<= (+ z 1.0) -5e+69)
     (* x z)
     (if (<= (+ z 1.0) -4.0)
       (* y z)
       (if (<= (+ z 1.0) 1.0)
         (+ x y)
         (if (or (<= (+ z 1.0) 1e+70) (not (<= (+ z 1.0) 2e+131)))
           (* x (+ z 1.0))
           (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -5e+97) {
		tmp = y * z;
	} else if ((z + 1.0) <= -5e+69) {
		tmp = x * z;
	} else if ((z + 1.0) <= -4.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1.0) {
		tmp = x + y;
	} else if (((z + 1.0) <= 1e+70) || !((z + 1.0) <= 2e+131)) {
		tmp = x * (z + 1.0);
	} 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) :: tmp
    if ((z + 1.0d0) <= (-5d+97)) then
        tmp = y * z
    else if ((z + 1.0d0) <= (-5d+69)) then
        tmp = x * z
    else if ((z + 1.0d0) <= (-4.0d0)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 1.0d0) then
        tmp = x + y
    else if (((z + 1.0d0) <= 1d+70) .or. (.not. ((z + 1.0d0) <= 2d+131))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -5e+97) {
		tmp = y * z;
	} else if ((z + 1.0) <= -5e+69) {
		tmp = x * z;
	} else if ((z + 1.0) <= -4.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1.0) {
		tmp = x + y;
	} else if (((z + 1.0) <= 1e+70) || !((z + 1.0) <= 2e+131)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -5e+97:
		tmp = y * z
	elif (z + 1.0) <= -5e+69:
		tmp = x * z
	elif (z + 1.0) <= -4.0:
		tmp = y * z
	elif (z + 1.0) <= 1.0:
		tmp = x + y
	elif ((z + 1.0) <= 1e+70) or not ((z + 1.0) <= 2e+131):
		tmp = x * (z + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -5e+97)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= -5e+69)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= -4.0)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 1.0)
		tmp = Float64(x + y);
	elseif ((Float64(z + 1.0) <= 1e+70) || !(Float64(z + 1.0) <= 2e+131))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z + 1.0) <= -5e+97)
		tmp = y * z;
	elseif ((z + 1.0) <= -5e+69)
		tmp = x * z;
	elseif ((z + 1.0) <= -4.0)
		tmp = y * z;
	elseif ((z + 1.0) <= 1.0)
		tmp = x + y;
	elseif (((z + 1.0) <= 1e+70) || ~(((z + 1.0) <= 2e+131)))
		tmp = x * (z + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -5e+97], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -5e+69], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -4.0], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[N[(z + 1.0), $MachinePrecision], 1e+70], N[Not[LessEqual[N[(z + 1.0), $MachinePrecision], 2e+131]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -4.99999999999999999e97 or -5.00000000000000036e69 < (+.f64 z #s(literal 1 binary64)) < -4 or 1.00000000000000007e70 < (+.f64 z #s(literal 1 binary64)) < 1.9999999999999998e131

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 85.8%

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

   4. Taylor expanded in z around inf 85.8%

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

   5. Taylor expanded in y around inf 47.3%

      \[\leadsto \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if -4.99999999999999999e97 < (+.f64 z #s(literal 1 binary64)) < -5.00000000000000036e69

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 84.9%

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

   7. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 66.8%

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

   9. Simplified 66.8%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

   if 1 < (+.f64 z #s(literal 1 binary64)) < 1.00000000000000007e70 or 1.9999999999999998e131 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 65.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -4:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+70} \lor \neg \left(z + 1 \leq 2 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+66}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 440000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+70} \lor \neg \left(z \leq 6.8 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.9e+94)
   (* y z)
   (if (<= z -3.7e+66)
     (* x z)
     (if (<= z -1.0)
       (* y z)
       (if (<= z 440000.0)
         (+ x y)
         (if (or (<= z 1.55e+70) (not (<= z 6.8e+133))) (* x z) (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.9e+94) {
		tmp = y * z;
	} else if (z <= -3.7e+66) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 440000.0) {
		tmp = x + y;
	} else if ((z <= 1.55e+70) || !(z <= 6.8e+133)) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.9d+94)) then
        tmp = y * z
    else if (z <= (-3.7d+66)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 440000.0d0) then
        tmp = x + y
    else if ((z <= 1.55d+70) .or. (.not. (z <= 6.8d+133))) then
        tmp = x * z
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.9e+94) {
		tmp = y * z;
	} else if (z <= -3.7e+66) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 440000.0) {
		tmp = x + y;
	} else if ((z <= 1.55e+70) || !(z <= 6.8e+133)) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.9e+94:
		tmp = y * z
	elif z <= -3.7e+66:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 440000.0:
		tmp = x + y
	elif (z <= 1.55e+70) or not (z <= 6.8e+133):
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.9e+94)
		tmp = Float64(y * z);
	elseif (z <= -3.7e+66)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 440000.0)
		tmp = Float64(x + y);
	elseif ((z <= 1.55e+70) || !(z <= 6.8e+133))
		tmp = Float64(x * z);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.9e+94)
		tmp = y * z;
	elseif (z <= -3.7e+66)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 440000.0)
		tmp = x + y;
	elseif ((z <= 1.55e+70) || ~((z <= 6.8e+133)))
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.9e+94], N[(y * z), $MachinePrecision], If[LessEqual[z, -3.7e+66], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 440000.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1.55e+70], N[Not[LessEqual[z, 6.8e+133]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8999999999999999e94 or -3.7e66 < z < -1 or 1.55000000000000015e70 < z < 6.79999999999999975e133

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 85.8%

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

   4. Taylor expanded in z around inf 85.8%

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

   5. Taylor expanded in y around inf 47.3%

      \[\leadsto \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if -5.8999999999999999e94 < z < -3.7e66 or 4.4e5 < z < 1.55000000000000015e70 or 6.79999999999999975e133 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.7%

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

      1. +-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x around inf 83.9%

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

   7. Taylor expanded in x around inf 60.4%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 60.4%

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

   9. Simplified 60.4%

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

   if -1 < z < 4.4e5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.7%

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

      1. +-commutative 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+66}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 440000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+70} \lor \neg \left(z \leq 6.8 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-33}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.3e-33)
   (* x z)
   (if (<= z 7.2e-242)
     x
     (if (<= z 3.1e-53) y (if (<= z 7.5e-5) x (if (<= z 0.28) y (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.3e-33) {
		tmp = x * z;
	} else if (z <= 7.2e-242) {
		tmp = x;
	} else if (z <= 3.1e-53) {
		tmp = y;
	} else if (z <= 7.5e-5) {
		tmp = x;
	} else if (z <= 0.28) {
		tmp = y;
	} else {
		tmp = x * 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 (z <= (-5.3d-33)) then
        tmp = x * z
    else if (z <= 7.2d-242) then
        tmp = x
    else if (z <= 3.1d-53) then
        tmp = y
    else if (z <= 7.5d-5) then
        tmp = x
    else if (z <= 0.28d0) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.3e-33) {
		tmp = x * z;
	} else if (z <= 7.2e-242) {
		tmp = x;
	} else if (z <= 3.1e-53) {
		tmp = y;
	} else if (z <= 7.5e-5) {
		tmp = x;
	} else if (z <= 0.28) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.3e-33:
		tmp = x * z
	elif z <= 7.2e-242:
		tmp = x
	elif z <= 3.1e-53:
		tmp = y
	elif z <= 7.5e-5:
		tmp = x
	elif z <= 0.28:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.3e-33)
		tmp = Float64(x * z);
	elseif (z <= 7.2e-242)
		tmp = x;
	elseif (z <= 3.1e-53)
		tmp = y;
	elseif (z <= 7.5e-5)
		tmp = x;
	elseif (z <= 0.28)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.3e-33)
		tmp = x * z;
	elseif (z <= 7.2e-242)
		tmp = x;
	elseif (z <= 3.1e-53)
		tmp = y;
	elseif (z <= 7.5e-5)
		tmp = x;
	elseif (z <= 0.28)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.3e-33], N[(x * z), $MachinePrecision], If[LessEqual[z, 7.2e-242], x, If[LessEqual[z, 3.1e-53], y, If[LessEqual[z, 7.5e-5], x, If[LessEqual[z, 0.28], y, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.29999999999999968e-33 or 0.28000000000000003 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.0%

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

      1. +-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in x around inf 84.5%

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

   7. Taylor expanded in x around inf 54.9%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 54.9%

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

   9. Simplified 54.9%

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

   if -5.29999999999999968e-33 < z < 7.20000000000000028e-242 or 3.10000000000000015e-53 < z < 7.49999999999999934e-5

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 49.4%

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

      1. +-commutative 49.4%

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

   7. Simplified 49.4%

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

   8. Taylor expanded in z around 0 47.6%

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

   if 7.20000000000000028e-242 < z < 3.10000000000000015e-53 or 7.49999999999999934e-5 < z < 0.28000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.3%

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

   4. Taylor expanded in z around 0 53.3%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-33}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -4 \lor \neg \left(z + 1 \leq 2\right):\\ \;\;\;\;z \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (+ z 1.0) -4.0) (not (<= (+ z 1.0) 2.0))) (* z (+ x y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((z + 1.0) <= -4.0) || !((z + 1.0) <= 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 (((z + 1.0d0) <= (-4.0d0)) .or. (.not. ((z + 1.0d0) <= 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 (((z + 1.0) <= -4.0) || !((z + 1.0) <= 2.0)) {
		tmp = z * (x + y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((z + 1.0) <= -4.0) or not ((z + 1.0) <= 2.0):
		tmp = z * (x + y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(z + 1.0) <= -4.0) || !(Float64(z + 1.0) <= 2.0))
		tmp = Float64(z * Float64(x + y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((z + 1.0) <= -4.0) || ~(((z + 1.0) <= 2.0)))
		tmp = z * (x + y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(z + 1.0), $MachinePrecision], -4.0], N[Not[LessEqual[N[(z + 1.0), $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 z #s(literal 1 binary64)) < -4 or 2 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.9%

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

      1. +-commutative 96.9%

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

   5. Simplified 96.9%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.4%

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

      1. +-commutative 96.4%

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

   5. Simplified 96.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -4 \lor \neg \left(z + 1 \leq 2\right):\\ \;\;\;\;z \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.4e-47) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.4e-47) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	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) :: tmp
    if (x <= (-7.4d-47)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.4e-47) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.4e-47:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.4e-47)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.4e-47)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.4e-47], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4000000000000001e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.6%

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

   if -7.4000000000000001e-47 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 59.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 32.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -5.5e-48) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-48) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d-48)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-48) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e-48:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e-48)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e-48)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e-48], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000047e-48

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 99.9%

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

      3. *-rgt-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 78.6%

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

      1. +-commutative 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in z around 0 33.7%

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

   if -5.50000000000000047e-48 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 59.0%

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

   4. Taylor expanded in z around 0 33.6%

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

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 26.1% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in x around inf 54.0%

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

   1. +-commutative 54.0%

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

7. Simplified 54.0%

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

8. Taylor expanded in z around 0 25.6%

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

9. Final simplification 25.6%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))