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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 9

Speedup: 1.0×

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

Specification

Math

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

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

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

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]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 51.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-249}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e-7)
   (* y z)
   (if (<= z -4e-111)
     y
     (if (<= z -5e-224)
       x
       (if (<= z 1.7e-297)
         y
         (if (<= z 4.1e-249)
           x
           (if (<= z 7.5e-104)
             y
             (if (<= z 1.25e-40) x (if (<= z 0.00017) y (* y z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e-7) {
		tmp = y * z;
	} else if (z <= -4e-111) {
		tmp = y;
	} else if (z <= -5e-224) {
		tmp = x;
	} else if (z <= 1.7e-297) {
		tmp = y;
	} else if (z <= 4.1e-249) {
		tmp = x;
	} else if (z <= 7.5e-104) {
		tmp = y;
	} else if (z <= 1.25e-40) {
		tmp = x;
	} else if (z <= 0.00017) {
		tmp = y;
	} 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 <= (-4.1d-7)) then
        tmp = y * z
    else if (z <= (-4d-111)) then
        tmp = y
    else if (z <= (-5d-224)) then
        tmp = x
    else if (z <= 1.7d-297) then
        tmp = y
    else if (z <= 4.1d-249) then
        tmp = x
    else if (z <= 7.5d-104) then
        tmp = y
    else if (z <= 1.25d-40) then
        tmp = x
    else if (z <= 0.00017d0) then
        tmp = y
    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 <= -4.1e-7) {
		tmp = y * z;
	} else if (z <= -4e-111) {
		tmp = y;
	} else if (z <= -5e-224) {
		tmp = x;
	} else if (z <= 1.7e-297) {
		tmp = y;
	} else if (z <= 4.1e-249) {
		tmp = x;
	} else if (z <= 7.5e-104) {
		tmp = y;
	} else if (z <= 1.25e-40) {
		tmp = x;
	} else if (z <= 0.00017) {
		tmp = y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e-7:
		tmp = y * z
	elif z <= -4e-111:
		tmp = y
	elif z <= -5e-224:
		tmp = x
	elif z <= 1.7e-297:
		tmp = y
	elif z <= 4.1e-249:
		tmp = x
	elif z <= 7.5e-104:
		tmp = y
	elif z <= 1.25e-40:
		tmp = x
	elif z <= 0.00017:
		tmp = y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e-7)
		tmp = Float64(y * z);
	elseif (z <= -4e-111)
		tmp = y;
	elseif (z <= -5e-224)
		tmp = x;
	elseif (z <= 1.7e-297)
		tmp = y;
	elseif (z <= 4.1e-249)
		tmp = x;
	elseif (z <= 7.5e-104)
		tmp = y;
	elseif (z <= 1.25e-40)
		tmp = x;
	elseif (z <= 0.00017)
		tmp = y;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e-7)
		tmp = y * z;
	elseif (z <= -4e-111)
		tmp = y;
	elseif (z <= -5e-224)
		tmp = x;
	elseif (z <= 1.7e-297)
		tmp = y;
	elseif (z <= 4.1e-249)
		tmp = x;
	elseif (z <= 7.5e-104)
		tmp = y;
	elseif (z <= 1.25e-40)
		tmp = x;
	elseif (z <= 0.00017)
		tmp = y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e-7], N[(y * z), $MachinePrecision], If[LessEqual[z, -4e-111], y, If[LessEqual[z, -5e-224], x, If[LessEqual[z, 1.7e-297], y, If[LessEqual[z, 4.1e-249], x, If[LessEqual[z, 7.5e-104], y, If[LessEqual[z, 1.25e-40], x, If[LessEqual[z, 0.00017], y, N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999999e-7 or 1.7e-4 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 51.8%

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

      1. +-commutative 51.8%

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

      2. distribute-lft-in 51.8%

         \[\leadsto \color{blue}{y \cdot z + y \cdot 1} \]

      3. *-rgt-identity 51.8%

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

   5. Applied egg-rr 51.8%

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

   6. Taylor expanded in z around inf 49.3%

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

   if -4.0999999999999999e-7 < z < -4.00000000000000035e-111 or -4.9999999999999999e-224 < z < 1.69999999999999991e-297 or 4.10000000000000004e-249 < z < 7.5e-104 or 1.24999999999999991e-40 < z < 1.7e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.8%

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

   4. Taylor expanded in z around 0 52.9%

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

   if -4.00000000000000035e-111 < z < -4.9999999999999999e-224 or 1.69999999999999991e-297 < z < 4.10000000000000004e-249 or 7.5e-104 < z < 1.24999999999999991e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.0%

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

   4. Taylor expanded in z around 0 68.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-249}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= z -1.7e+231)
     (* y z)
     (if (<= z -1.7e+148)
       (* x z)
       (if (<= z -4.1e+73)
         (* y z)
         (if (<= z -2.7e-9)
           t_0
           (if (<= z 9.2e-7) (+ x y) (if (<= z 6e+191) t_0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -1.7e+231) {
		tmp = y * z;
	} else if (z <= -1.7e+148) {
		tmp = x * z;
	} else if (z <= -4.1e+73) {
		tmp = y * z;
	} else if (z <= -2.7e-9) {
		tmp = t_0;
	} else if (z <= 9.2e-7) {
		tmp = x + y;
	} else if (z <= 6e+191) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z + 1.0d0)
    if (z <= (-1.7d+231)) then
        tmp = y * z
    else if (z <= (-1.7d+148)) then
        tmp = x * z
    else if (z <= (-4.1d+73)) then
        tmp = y * z
    else if (z <= (-2.7d-9)) then
        tmp = t_0
    else if (z <= 9.2d-7) then
        tmp = x + y
    else if (z <= 6d+191) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -1.7e+231) {
		tmp = y * z;
	} else if (z <= -1.7e+148) {
		tmp = x * z;
	} else if (z <= -4.1e+73) {
		tmp = y * z;
	} else if (z <= -2.7e-9) {
		tmp = t_0;
	} else if (z <= 9.2e-7) {
		tmp = x + y;
	} else if (z <= 6e+191) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if z <= -1.7e+231:
		tmp = y * z
	elif z <= -1.7e+148:
		tmp = x * z
	elif z <= -4.1e+73:
		tmp = y * z
	elif z <= -2.7e-9:
		tmp = t_0
	elif z <= 9.2e-7:
		tmp = x + y
	elif z <= 6e+191:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (z <= -1.7e+231)
		tmp = Float64(y * z);
	elseif (z <= -1.7e+148)
		tmp = Float64(x * z);
	elseif (z <= -4.1e+73)
		tmp = Float64(y * z);
	elseif (z <= -2.7e-9)
		tmp = t_0;
	elseif (z <= 9.2e-7)
		tmp = Float64(x + y);
	elseif (z <= 6e+191)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if (z <= -1.7e+231)
		tmp = y * z;
	elseif (z <= -1.7e+148)
		tmp = x * z;
	elseif (z <= -4.1e+73)
		tmp = y * z;
	elseif (z <= -2.7e-9)
		tmp = t_0;
	elseif (z <= 9.2e-7)
		tmp = x + y;
	elseif (z <= 6e+191)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+231], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.7e+148], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.1e+73], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.7e-9], t$95$0, If[LessEqual[z, 9.2e-7], N[(x + y), $MachinePrecision], If[LessEqual[z, 6e+191], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7e231 or -1.7000000000000001e148 < z < -4.0999999999999998e73 or 5.9999999999999995e191 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. distribute-lft-in 55.8%

         \[\leadsto \color{blue}{y \cdot z + y \cdot 1} \]

      3. *-rgt-identity 55.8%

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

   5. Applied egg-rr 55.8%

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

   6. Taylor expanded in z around inf 55.8%

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

   if -1.7e231 < z < -1.7000000000000001e148

   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%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in y around 0 63.2%

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

      1. *-commutative 63.2%

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

   8. Simplified 63.2%

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

   if -4.0999999999999998e73 < z < -2.7000000000000002e-9 or 9.1999999999999998e-7 < z < 5.9999999999999995e191

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 49.2%

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

   if -2.7000000000000002e-9 < z < 9.1999999999999998e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 660:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+190}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.35e+231)
   (* y z)
   (if (<= z -1.7e+148)
     (* x z)
     (if (<= z -4.8e+72)
       (* y z)
       (if (<= z -1.0)
         (* x z)
         (if (<= z 660.0) (+ x y) (if (<= z 6.6e+190) (* x z) (* y z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.35e+231) {
		tmp = y * z;
	} else if (z <= -1.7e+148) {
		tmp = x * z;
	} else if (z <= -4.8e+72) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 660.0) {
		tmp = x + y;
	} else if (z <= 6.6e+190) {
		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 <= (-1.35d+231)) then
        tmp = y * z
    else if (z <= (-1.7d+148)) then
        tmp = x * z
    else if (z <= (-4.8d+72)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 660.0d0) then
        tmp = x + y
    else if (z <= 6.6d+190) 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 <= -1.35e+231) {
		tmp = y * z;
	} else if (z <= -1.7e+148) {
		tmp = x * z;
	} else if (z <= -4.8e+72) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 660.0) {
		tmp = x + y;
	} else if (z <= 6.6e+190) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.35e+231:
		tmp = y * z
	elif z <= -1.7e+148:
		tmp = x * z
	elif z <= -4.8e+72:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 660.0:
		tmp = x + y
	elif z <= 6.6e+190:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.35e+231)
		tmp = Float64(y * z);
	elseif (z <= -1.7e+148)
		tmp = Float64(x * z);
	elseif (z <= -4.8e+72)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 660.0)
		tmp = Float64(x + y);
	elseif (z <= 6.6e+190)
		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 <= -1.35e+231)
		tmp = y * z;
	elseif (z <= -1.7e+148)
		tmp = x * z;
	elseif (z <= -4.8e+72)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 660.0)
		tmp = x + y;
	elseif (z <= 6.6e+190)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.35e+231], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.7e+148], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.8e+72], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 660.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 6.6e+190], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e231 or -1.7000000000000001e148 < z < -4.8000000000000002e72 or 6.6e190 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. distribute-lft-in 55.8%

         \[\leadsto \color{blue}{y \cdot z + y \cdot 1} \]

      3. *-rgt-identity 55.8%

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

   5. Applied egg-rr 55.8%

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

   6. Taylor expanded in z around inf 55.8%

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

   if -1.35e231 < z < -1.7000000000000001e148 or -4.8000000000000002e72 < z < -1 or 660 < z < 6.6e190

   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%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 99.2%

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

   6. Taylor expanded in y around 0 51.6%

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

      1. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if -1 < z < 660

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 660:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+190}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 32.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-125}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.78 \cdot 10^{+59}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-32)
   x
   (if (<= y -1.12e-125)
     (* x z)
     (if (<= y -2.05e-184)
       x
       (if (<= y 1.8e-53) (* x z) (if (<= y 1.78e+59) y (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-32) {
		tmp = x;
	} else if (y <= -1.12e-125) {
		tmp = x * z;
	} else if (y <= -2.05e-184) {
		tmp = x;
	} else if (y <= 1.8e-53) {
		tmp = x * z;
	} else if (y <= 1.78e+59) {
		tmp = y;
	} 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 (y <= (-4d-32)) then
        tmp = x
    else if (y <= (-1.12d-125)) then
        tmp = x * z
    else if (y <= (-2.05d-184)) then
        tmp = x
    else if (y <= 1.8d-53) then
        tmp = x * z
    else if (y <= 1.78d+59) then
        tmp = y
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-32) {
		tmp = x;
	} else if (y <= -1.12e-125) {
		tmp = x * z;
	} else if (y <= -2.05e-184) {
		tmp = x;
	} else if (y <= 1.8e-53) {
		tmp = x * z;
	} else if (y <= 1.78e+59) {
		tmp = y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e-32:
		tmp = x
	elif y <= -1.12e-125:
		tmp = x * z
	elif y <= -2.05e-184:
		tmp = x
	elif y <= 1.8e-53:
		tmp = x * z
	elif y <= 1.78e+59:
		tmp = y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e-32)
		tmp = x;
	elseif (y <= -1.12e-125)
		tmp = Float64(x * z);
	elseif (y <= -2.05e-184)
		tmp = x;
	elseif (y <= 1.8e-53)
		tmp = Float64(x * z);
	elseif (y <= 1.78e+59)
		tmp = y;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e-32)
		tmp = x;
	elseif (y <= -1.12e-125)
		tmp = x * z;
	elseif (y <= -2.05e-184)
		tmp = x;
	elseif (y <= 1.8e-53)
		tmp = x * z;
	elseif (y <= 1.78e+59)
		tmp = y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e-32], x, If[LessEqual[y, -1.12e-125], N[(x * z), $MachinePrecision], If[LessEqual[y, -2.05e-184], x, If[LessEqual[y, 1.8e-53], N[(x * z), $MachinePrecision], If[LessEqual[y, 1.78e+59], y, N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.00000000000000022e-32 or -1.11999999999999997e-125 < y < -2.05e-184

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 42.1%

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

   4. Taylor expanded in z around 0 21.9%

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

   if -4.00000000000000022e-32 < y < -1.11999999999999997e-125 or -2.05e-184 < y < 1.7999999999999999e-53

   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%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 60.5%

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

   6. Taylor expanded in y around 0 40.6%

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

      1. *-commutative 40.6%

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

   8. Simplified 40.6%

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

   if 1.7999999999999999e-53 < y < 1.78e59

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 43.2%

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

   4. Taylor expanded in z around 0 29.6%

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

   if 1.78e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. distribute-lft-in 84.1%

         \[\leadsto \color{blue}{y \cdot z + y \cdot 1} \]

      3. *-rgt-identity 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in z around inf 47.3%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-125}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.78 \cdot 10^{+59}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < 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 97.2%

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

      1. +-commutative 97.2%

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

   5. Simplified 97.2%

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

   if -1 < z < 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 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 97.5%

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

Alternative 7: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5e-84) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5e-84) {
		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 (y <= 2.5d-84) 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 (y <= 2.5e-84) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5e-84:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5e-84)
		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 (y <= 2.5e-84)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5e-84], 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 y < 2.5000000000000001e-84

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.2%

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

   if 2.5000000000000001e-84 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 66.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 32.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 4.1e-81) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.1e-81) {
		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 (y <= 4.1d-81) 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 (y <= 4.1e-81) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.1e-81:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.1e-81)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.1e-81)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.1e-81], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 4.09999999999999984e-81

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.5%

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

   4. Taylor expanded in z around 0 32.4%

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

   if 4.09999999999999984e-81 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 66.1%

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

   4. Taylor expanded in z around 0 33.6%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 26.9% 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. Taylor expanded in x around inf 53.8%

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

4. Taylor expanded in z around 0 28.3%

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

5. Final simplification 28.3%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))