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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 9

Speedup: 1.0×

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

• could not determine a ground truth

  1. x = 3.1923413041848926e+238
  2. y = 9.203367067412205e+238
  3. z = -1.0726066697662055e-190

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: 50.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -29000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+190}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.22e+231)
   (* y z)
   (if (<= z -2.2e+148)
     (* x z)
     (if (<= z -9.5e+72)
       (* y z)
       (if (<= z -29000000.0)
         (* x z)
         (if (<= z -2.8e-37)
           x
           (if (<= z -4.1e-113)
             y
             (if (<= z -7.5e-226)
               x
               (if (<= z 1.8e-297)
                 y
                 (if (<= z 9.5e-250)
                   x
                   (if (<= z 1.7e-104)
                     y
                     (if (<= z 5.4e-40)
                       x
                       (if (<= z 0.00017)
                         y
                         (if (<= z 5.9e+190) (* x z) (* y z)))))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.22e+231) {
		tmp = y * z;
	} else if (z <= -2.2e+148) {
		tmp = x * z;
	} else if (z <= -9.5e+72) {
		tmp = y * z;
	} else if (z <= -29000000.0) {
		tmp = x * z;
	} else if (z <= -2.8e-37) {
		tmp = x;
	} else if (z <= -4.1e-113) {
		tmp = y;
	} else if (z <= -7.5e-226) {
		tmp = x;
	} else if (z <= 1.8e-297) {
		tmp = y;
	} else if (z <= 9.5e-250) {
		tmp = x;
	} else if (z <= 1.7e-104) {
		tmp = y;
	} else if (z <= 5.4e-40) {
		tmp = x;
	} else if (z <= 0.00017) {
		tmp = y;
	} else if (z <= 5.9e+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 <= (-1.22d+231)) then
        tmp = y * z
    else if (z <= (-2.2d+148)) then
        tmp = x * z
    else if (z <= (-9.5d+72)) then
        tmp = y * z
    else if (z <= (-29000000.0d0)) then
        tmp = x * z
    else if (z <= (-2.8d-37)) then
        tmp = x
    else if (z <= (-4.1d-113)) then
        tmp = y
    else if (z <= (-7.5d-226)) then
        tmp = x
    else if (z <= 1.8d-297) then
        tmp = y
    else if (z <= 9.5d-250) then
        tmp = x
    else if (z <= 1.7d-104) then
        tmp = y
    else if (z <= 5.4d-40) then
        tmp = x
    else if (z <= 0.00017d0) then
        tmp = y
    else if (z <= 5.9d+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 <= -1.22e+231) {
		tmp = y * z;
	} else if (z <= -2.2e+148) {
		tmp = x * z;
	} else if (z <= -9.5e+72) {
		tmp = y * z;
	} else if (z <= -29000000.0) {
		tmp = x * z;
	} else if (z <= -2.8e-37) {
		tmp = x;
	} else if (z <= -4.1e-113) {
		tmp = y;
	} else if (z <= -7.5e-226) {
		tmp = x;
	} else if (z <= 1.8e-297) {
		tmp = y;
	} else if (z <= 9.5e-250) {
		tmp = x;
	} else if (z <= 1.7e-104) {
		tmp = y;
	} else if (z <= 5.4e-40) {
		tmp = x;
	} else if (z <= 0.00017) {
		tmp = y;
	} else if (z <= 5.9e+190) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.22e+231:
		tmp = y * z
	elif z <= -2.2e+148:
		tmp = x * z
	elif z <= -9.5e+72:
		tmp = y * z
	elif z <= -29000000.0:
		tmp = x * z
	elif z <= -2.8e-37:
		tmp = x
	elif z <= -4.1e-113:
		tmp = y
	elif z <= -7.5e-226:
		tmp = x
	elif z <= 1.8e-297:
		tmp = y
	elif z <= 9.5e-250:
		tmp = x
	elif z <= 1.7e-104:
		tmp = y
	elif z <= 5.4e-40:
		tmp = x
	elif z <= 0.00017:
		tmp = y
	elif z <= 5.9e+190:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.22e+231)
		tmp = Float64(y * z);
	elseif (z <= -2.2e+148)
		tmp = Float64(x * z);
	elseif (z <= -9.5e+72)
		tmp = Float64(y * z);
	elseif (z <= -29000000.0)
		tmp = Float64(x * z);
	elseif (z <= -2.8e-37)
		tmp = x;
	elseif (z <= -4.1e-113)
		tmp = y;
	elseif (z <= -7.5e-226)
		tmp = x;
	elseif (z <= 1.8e-297)
		tmp = y;
	elseif (z <= 9.5e-250)
		tmp = x;
	elseif (z <= 1.7e-104)
		tmp = y;
	elseif (z <= 5.4e-40)
		tmp = x;
	elseif (z <= 0.00017)
		tmp = y;
	elseif (z <= 5.9e+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 <= -1.22e+231)
		tmp = y * z;
	elseif (z <= -2.2e+148)
		tmp = x * z;
	elseif (z <= -9.5e+72)
		tmp = y * z;
	elseif (z <= -29000000.0)
		tmp = x * z;
	elseif (z <= -2.8e-37)
		tmp = x;
	elseif (z <= -4.1e-113)
		tmp = y;
	elseif (z <= -7.5e-226)
		tmp = x;
	elseif (z <= 1.8e-297)
		tmp = y;
	elseif (z <= 9.5e-250)
		tmp = x;
	elseif (z <= 1.7e-104)
		tmp = y;
	elseif (z <= 5.4e-40)
		tmp = x;
	elseif (z <= 0.00017)
		tmp = y;
	elseif (z <= 5.9e+190)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.22e+231], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.2e+148], N[(x * z), $MachinePrecision], If[LessEqual[z, -9.5e+72], N[(y * z), $MachinePrecision], If[LessEqual[z, -29000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.8e-37], x, If[LessEqual[z, -4.1e-113], y, If[LessEqual[z, -7.5e-226], x, If[LessEqual[z, 1.8e-297], y, If[LessEqual[z, 9.5e-250], x, If[LessEqual[z, 1.7e-104], y, If[LessEqual[z, 5.4e-40], x, If[LessEqual[z, 0.00017], y, If[LessEqual[z, 5.9e+190], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.21999999999999998e231 or -2.1999999999999999e148 < z < -9.50000000000000054e72 or 5.89999999999999972e190 < 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 56.7%

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

      1. +-commutative 56.7%

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

      2. distribute-lft-in 56.7%

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

      3. *-rgt-identity 56.7%

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

   5. Applied egg-rr 56.7%

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

   6. Taylor expanded in z around inf 56.7%

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

   if -1.21999999999999998e231 < z < -2.1999999999999999e148 or -9.50000000000000054e72 < z < -2.9e7 or 1.7e-4 < z < 5.89999999999999972e190

   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 95.9%

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

   6. Taylor expanded in y around 0 52.9%

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

      1. *-commutative 52.9%

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

   8. Simplified 52.9%

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

   if -2.9e7 < z < -2.8000000000000001e-37 or -4.1e-113 < z < -7.50000000000000044e-226 or 1.79999999999999997e-297 < z < 9.5000000000000002e-250 or 1.70000000000000008e-104 < z < 5.4e-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 62.5%

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

   4. Taylor expanded in z around 0 62.4%

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

   if -2.8000000000000001e-37 < z < -4.1e-113 or -7.50000000000000044e-226 < z < 1.79999999999999997e-297 or 9.5000000000000002e-250 < z < 1.70000000000000008e-104 or 5.4e-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 53.5%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -29000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+190}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e-7)
   (* y z)
   (if (<= z -4.8e-113)
     y
     (if (<= z -1.4e-224)
       x
       (if (<= z 4.2e-297)
         y
         (if (<= z 6e-250)
           x
           (if (<= z 1e-103)
             y
             (if (<= z 1.24e-39) 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 <= -4.8e-113) {
		tmp = y;
	} else if (z <= -1.4e-224) {
		tmp = x;
	} else if (z <= 4.2e-297) {
		tmp = y;
	} else if (z <= 6e-250) {
		tmp = x;
	} else if (z <= 1e-103) {
		tmp = y;
	} else if (z <= 1.24e-39) {
		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 <= (-4.8d-113)) then
        tmp = y
    else if (z <= (-1.4d-224)) then
        tmp = x
    else if (z <= 4.2d-297) then
        tmp = y
    else if (z <= 6d-250) then
        tmp = x
    else if (z <= 1d-103) then
        tmp = y
    else if (z <= 1.24d-39) 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 <= -4.8e-113) {
		tmp = y;
	} else if (z <= -1.4e-224) {
		tmp = x;
	} else if (z <= 4.2e-297) {
		tmp = y;
	} else if (z <= 6e-250) {
		tmp = x;
	} else if (z <= 1e-103) {
		tmp = y;
	} else if (z <= 1.24e-39) {
		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 <= -4.8e-113:
		tmp = y
	elif z <= -1.4e-224:
		tmp = x
	elif z <= 4.2e-297:
		tmp = y
	elif z <= 6e-250:
		tmp = x
	elif z <= 1e-103:
		tmp = y
	elif z <= 1.24e-39:
		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 <= -4.8e-113)
		tmp = y;
	elseif (z <= -1.4e-224)
		tmp = x;
	elseif (z <= 4.2e-297)
		tmp = y;
	elseif (z <= 6e-250)
		tmp = x;
	elseif (z <= 1e-103)
		tmp = y;
	elseif (z <= 1.24e-39)
		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 <= -4.8e-113)
		tmp = y;
	elseif (z <= -1.4e-224)
		tmp = x;
	elseif (z <= 4.2e-297)
		tmp = y;
	elseif (z <= 6e-250)
		tmp = x;
	elseif (z <= 1e-103)
		tmp = y;
	elseif (z <= 1.24e-39)
		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, -4.8e-113], y, If[LessEqual[z, -1.4e-224], x, If[LessEqual[z, 4.2e-297], y, If[LessEqual[z, 6e-250], x, If[LessEqual[z, 1e-103], y, If[LessEqual[z, 1.24e-39], 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 51.5%

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

      1. +-commutative 51.5%

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

      2. distribute-lft-in 51.5%

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

      3. *-rgt-identity 51.5%

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

   5. Applied egg-rr 51.5%

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

   6. Taylor expanded in z around inf 49.0%

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

   if -4.0999999999999999e-7 < z < -4.80000000000000024e-113 or -1.3999999999999999e-224 < z < 4.20000000000000027e-297 or 6.00000000000000032e-250 < z < 9.99999999999999958e-104 or 1.24000000000000004e-39 < 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 54.4%

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

   4. Taylor expanded in z around 0 53.6%

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

   if -4.80000000000000024e-113 < z < -1.3999999999999999e-224 or 4.20000000000000027e-297 < z < 6.00000000000000032e-250 or 9.99999999999999958e-104 < z < 1.24000000000000004e-39

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -98000000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+191}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+231)
   (* y z)
   (if (<= z -1.45e+148)
     (* x z)
     (if (<= z -6e+72)
       (* y z)
       (if (<= z -98000000000000.0)
         (* x z)
         (if (<= z -1.0)
           (* y z)
           (if (<= z 550.0) (+ x y) (if (<= z 2.2e+191) (* x z) (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+231) {
		tmp = y * z;
	} else if (z <= -1.45e+148) {
		tmp = x * z;
	} else if (z <= -6e+72) {
		tmp = y * z;
	} else if (z <= -98000000000000.0) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 550.0) {
		tmp = x + y;
	} else if (z <= 2.2e+191) {
		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 <= (-2.5d+231)) then
        tmp = y * z
    else if (z <= (-1.45d+148)) then
        tmp = x * z
    else if (z <= (-6d+72)) then
        tmp = y * z
    else if (z <= (-98000000000000.0d0)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 550.0d0) then
        tmp = x + y
    else if (z <= 2.2d+191) 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 <= -2.5e+231) {
		tmp = y * z;
	} else if (z <= -1.45e+148) {
		tmp = x * z;
	} else if (z <= -6e+72) {
		tmp = y * z;
	} else if (z <= -98000000000000.0) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 550.0) {
		tmp = x + y;
	} else if (z <= 2.2e+191) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+231:
		tmp = y * z
	elif z <= -1.45e+148:
		tmp = x * z
	elif z <= -6e+72:
		tmp = y * z
	elif z <= -98000000000000.0:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 550.0:
		tmp = x + y
	elif z <= 2.2e+191:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+231)
		tmp = Float64(y * z);
	elseif (z <= -1.45e+148)
		tmp = Float64(x * z);
	elseif (z <= -6e+72)
		tmp = Float64(y * z);
	elseif (z <= -98000000000000.0)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 550.0)
		tmp = Float64(x + y);
	elseif (z <= 2.2e+191)
		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 <= -2.5e+231)
		tmp = y * z;
	elseif (z <= -1.45e+148)
		tmp = x * z;
	elseif (z <= -6e+72)
		tmp = y * z;
	elseif (z <= -98000000000000.0)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 550.0)
		tmp = x + y;
	elseif (z <= 2.2e+191)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+231], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.45e+148], N[(x * z), $MachinePrecision], If[LessEqual[z, -6e+72], N[(y * z), $MachinePrecision], If[LessEqual[z, -98000000000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 550.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.2e+191], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000014e231 or -1.45e148 < z < -6.00000000000000006e72 or -9.8e13 < z < -1 or 2.2e191 < 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 58.2%

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

      1. +-commutative 58.2%

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

      2. distribute-lft-in 58.1%

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

      3. *-rgt-identity 58.1%

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

   5. Applied egg-rr 58.1%

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

   6. Taylor expanded in z around inf 56.2%

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

   if -2.50000000000000014e231 < z < -1.45e148 or -6.00000000000000006e72 < z < -9.8e13 or 550 < z < 2.2e191

   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 54.4%

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

      1. *-commutative 54.4%

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

   8. Simplified 54.4%

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

   if -1 < z < 550

   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 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -98000000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+191}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+232}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+190}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= z -6.5e+232)
     (* y z)
     (if (<= z -1.8e+148)
       (* x z)
       (if (<= z -4.6e+72)
         (* y z)
         (if (<= z -1.75e-9)
           t_0
           (if (<= z 3.2e-6) (+ x y) (if (<= z 8.4e+190) t_0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -6.5e+232) {
		tmp = y * z;
	} else if (z <= -1.8e+148) {
		tmp = x * z;
	} else if (z <= -4.6e+72) {
		tmp = y * z;
	} else if (z <= -1.75e-9) {
		tmp = t_0;
	} else if (z <= 3.2e-6) {
		tmp = x + y;
	} else if (z <= 8.4e+190) {
		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 <= (-6.5d+232)) then
        tmp = y * z
    else if (z <= (-1.8d+148)) then
        tmp = x * z
    else if (z <= (-4.6d+72)) then
        tmp = y * z
    else if (z <= (-1.75d-9)) then
        tmp = t_0
    else if (z <= 3.2d-6) then
        tmp = x + y
    else if (z <= 8.4d+190) 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 <= -6.5e+232) {
		tmp = y * z;
	} else if (z <= -1.8e+148) {
		tmp = x * z;
	} else if (z <= -4.6e+72) {
		tmp = y * z;
	} else if (z <= -1.75e-9) {
		tmp = t_0;
	} else if (z <= 3.2e-6) {
		tmp = x + y;
	} else if (z <= 8.4e+190) {
		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 <= -6.5e+232:
		tmp = y * z
	elif z <= -1.8e+148:
		tmp = x * z
	elif z <= -4.6e+72:
		tmp = y * z
	elif z <= -1.75e-9:
		tmp = t_0
	elif z <= 3.2e-6:
		tmp = x + y
	elif z <= 8.4e+190:
		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 <= -6.5e+232)
		tmp = Float64(y * z);
	elseif (z <= -1.8e+148)
		tmp = Float64(x * z);
	elseif (z <= -4.6e+72)
		tmp = Float64(y * z);
	elseif (z <= -1.75e-9)
		tmp = t_0;
	elseif (z <= 3.2e-6)
		tmp = Float64(x + y);
	elseif (z <= 8.4e+190)
		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 <= -6.5e+232)
		tmp = y * z;
	elseif (z <= -1.8e+148)
		tmp = x * z;
	elseif (z <= -4.6e+72)
		tmp = y * z;
	elseif (z <= -1.75e-9)
		tmp = t_0;
	elseif (z <= 3.2e-6)
		tmp = x + y;
	elseif (z <= 8.4e+190)
		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, -6.5e+232], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.8e+148], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.6e+72], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.75e-9], t$95$0, If[LessEqual[z, 3.2e-6], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.4e+190], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.50000000000000016e232 or -1.80000000000000003e148 < z < -4.6e72 or 8.4000000000000003e190 < 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 56.7%

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

      1. +-commutative 56.7%

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

      2. distribute-lft-in 56.7%

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

      3. *-rgt-identity 56.7%

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

   5. Applied egg-rr 56.7%

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

   6. Taylor expanded in z around inf 56.7%

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

   if -6.50000000000000016e232 < z < -1.80000000000000003e148

   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 -4.6e72 < z < -1.75e-9 or 3.1999999999999999e-6 < z < 8.4000000000000003e190

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 50.9%

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

   if -1.75e-9 < z < 3.1999999999999999e-6

   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 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+232}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.36 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.36e-86) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.36e-86) {
		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 <= 1.36d-86) 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 <= 1.36e-86) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.36e-86:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.36e-86)
		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 <= 1.36e-86)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.36e-86], 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 < 1.3599999999999999e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.4%

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

   if 1.3599999999999999e-86 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.36 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 32.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.15e-77) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.15e-77) {
		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 <= 1.15d-77) 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 <= 1.15e-77) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.15e-77:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.15e-77)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.15e-77)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.15e-77], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.14999999999999999e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.1%

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

   4. Taylor expanded in z around 0 33.0%

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

   if 1.14999999999999999e-77 < 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 67.1%

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

   4. Taylor expanded in z around 0 34.7%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
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 28.4%

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

5. Final simplification 28.4%

   \[\leadsto x \]
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)))