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

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 10

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, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \left(x + y\right) + z \cdot \left(x + y\right) \]

Alternative 2: 50.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-126}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-298}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* x z)
   (if (<= z -6e-126)
     y
     (if (<= z -3.7e-252)
       x
       (if (<= z -2.6e-298)
         y
         (if (<= z 2.8e-268)
           x
           (if (<= z 1.3e-191)
             y
             (if (<= z 9.8e-133)
               x
               (if (<= z 4.4e-57)
                 y
                 (if (<= z 29000000000.0) x (* x z)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -6e-126) {
		tmp = y;
	} else if (z <= -3.7e-252) {
		tmp = x;
	} else if (z <= -2.6e-298) {
		tmp = y;
	} else if (z <= 2.8e-268) {
		tmp = x;
	} else if (z <= 1.3e-191) {
		tmp = y;
	} else if (z <= 9.8e-133) {
		tmp = x;
	} else if (z <= 4.4e-57) {
		tmp = y;
	} else if (z <= 29000000000.0) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = x * z
    else if (z <= (-6d-126)) then
        tmp = y
    else if (z <= (-3.7d-252)) then
        tmp = x
    else if (z <= (-2.6d-298)) then
        tmp = y
    else if (z <= 2.8d-268) then
        tmp = x
    else if (z <= 1.3d-191) then
        tmp = y
    else if (z <= 9.8d-133) then
        tmp = x
    else if (z <= 4.4d-57) then
        tmp = y
    else if (z <= 29000000000.0d0) then
        tmp = x
    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 <= -1.0) {
		tmp = x * z;
	} else if (z <= -6e-126) {
		tmp = y;
	} else if (z <= -3.7e-252) {
		tmp = x;
	} else if (z <= -2.6e-298) {
		tmp = y;
	} else if (z <= 2.8e-268) {
		tmp = x;
	} else if (z <= 1.3e-191) {
		tmp = y;
	} else if (z <= 9.8e-133) {
		tmp = x;
	} else if (z <= 4.4e-57) {
		tmp = y;
	} else if (z <= 29000000000.0) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= -6e-126:
		tmp = y
	elif z <= -3.7e-252:
		tmp = x
	elif z <= -2.6e-298:
		tmp = y
	elif z <= 2.8e-268:
		tmp = x
	elif z <= 1.3e-191:
		tmp = y
	elif z <= 9.8e-133:
		tmp = x
	elif z <= 4.4e-57:
		tmp = y
	elif z <= 29000000000.0:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= -6e-126)
		tmp = y;
	elseif (z <= -3.7e-252)
		tmp = x;
	elseif (z <= -2.6e-298)
		tmp = y;
	elseif (z <= 2.8e-268)
		tmp = x;
	elseif (z <= 1.3e-191)
		tmp = y;
	elseif (z <= 9.8e-133)
		tmp = x;
	elseif (z <= 4.4e-57)
		tmp = y;
	elseif (z <= 29000000000.0)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= -6e-126)
		tmp = y;
	elseif (z <= -3.7e-252)
		tmp = x;
	elseif (z <= -2.6e-298)
		tmp = y;
	elseif (z <= 2.8e-268)
		tmp = x;
	elseif (z <= 1.3e-191)
		tmp = y;
	elseif (z <= 9.8e-133)
		tmp = x;
	elseif (z <= 4.4e-57)
		tmp = y;
	elseif (z <= 29000000000.0)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -6e-126], y, If[LessEqual[z, -3.7e-252], x, If[LessEqual[z, -2.6e-298], y, If[LessEqual[z, 2.8e-268], x, If[LessEqual[z, 1.3e-191], y, If[LessEqual[z, 9.8e-133], x, If[LessEqual[z, 4.4e-57], y, If[LessEqual[z, 29000000000.0], x, N[(x * z), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 2.9e10 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 57.3%

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

      1. +-commutative 57.3%

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

      2. distribute-lft-in 57.3%

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

      3. *-rgt-identity 57.3%

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

   4. Applied egg-rr 57.3%

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

   5. Taylor expanded in z around inf 56.6%

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

   if -1 < z < -6.0000000000000003e-126 or -3.7000000000000001e-252 < z < -2.5999999999999999e-298 or 2.80000000000000015e-268 < z < 1.29999999999999993e-191 or 9.79999999999999992e-133 < z < 4.39999999999999997e-57

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 46.1%

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

   3. Taylor expanded in z around 0 46.1%

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

   if -6.0000000000000003e-126 < z < -3.7000000000000001e-252 or -2.5999999999999999e-298 < z < 2.80000000000000015e-268 or 1.29999999999999993e-191 < z < 9.79999999999999992e-133 or 4.39999999999999997e-57 < z < 2.9e10

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 47.4%

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

   3. Taylor expanded in z around 0 47.0%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-126}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-298}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-299}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* y z)
   (if (<= z -1.8e-124)
     y
     (if (<= z -1.4e-247)
       x
       (if (<= z -8.4e-299)
         y
         (if (<= z 2.2e-269)
           x
           (if (<= z 6e-192)
             y
             (if (<= z 1.75e-133)
               x
               (if (<= z 4.4e-66)
                 y
                 (if (<= z 29000000000.0) x (* x z)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -1.8e-124) {
		tmp = y;
	} else if (z <= -1.4e-247) {
		tmp = x;
	} else if (z <= -8.4e-299) {
		tmp = y;
	} else if (z <= 2.2e-269) {
		tmp = x;
	} else if (z <= 6e-192) {
		tmp = y;
	} else if (z <= 1.75e-133) {
		tmp = x;
	} else if (z <= 4.4e-66) {
		tmp = y;
	} else if (z <= 29000000000.0) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = y * z
    else if (z <= (-1.8d-124)) then
        tmp = y
    else if (z <= (-1.4d-247)) then
        tmp = x
    else if (z <= (-8.4d-299)) then
        tmp = y
    else if (z <= 2.2d-269) then
        tmp = x
    else if (z <= 6d-192) then
        tmp = y
    else if (z <= 1.75d-133) then
        tmp = x
    else if (z <= 4.4d-66) then
        tmp = y
    else if (z <= 29000000000.0d0) then
        tmp = x
    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 <= -1.0) {
		tmp = y * z;
	} else if (z <= -1.8e-124) {
		tmp = y;
	} else if (z <= -1.4e-247) {
		tmp = x;
	} else if (z <= -8.4e-299) {
		tmp = y;
	} else if (z <= 2.2e-269) {
		tmp = x;
	} else if (z <= 6e-192) {
		tmp = y;
	} else if (z <= 1.75e-133) {
		tmp = x;
	} else if (z <= 4.4e-66) {
		tmp = y;
	} else if (z <= 29000000000.0) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= -1.8e-124:
		tmp = y
	elif z <= -1.4e-247:
		tmp = x
	elif z <= -8.4e-299:
		tmp = y
	elif z <= 2.2e-269:
		tmp = x
	elif z <= 6e-192:
		tmp = y
	elif z <= 1.75e-133:
		tmp = x
	elif z <= 4.4e-66:
		tmp = y
	elif z <= 29000000000.0:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= -1.8e-124)
		tmp = y;
	elseif (z <= -1.4e-247)
		tmp = x;
	elseif (z <= -8.4e-299)
		tmp = y;
	elseif (z <= 2.2e-269)
		tmp = x;
	elseif (z <= 6e-192)
		tmp = y;
	elseif (z <= 1.75e-133)
		tmp = x;
	elseif (z <= 4.4e-66)
		tmp = y;
	elseif (z <= 29000000000.0)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = y * z;
	elseif (z <= -1.8e-124)
		tmp = y;
	elseif (z <= -1.4e-247)
		tmp = x;
	elseif (z <= -8.4e-299)
		tmp = y;
	elseif (z <= 2.2e-269)
		tmp = x;
	elseif (z <= 6e-192)
		tmp = y;
	elseif (z <= 1.75e-133)
		tmp = x;
	elseif (z <= 4.4e-66)
		tmp = y;
	elseif (z <= 29000000000.0)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.8e-124], y, If[LessEqual[z, -1.4e-247], x, If[LessEqual[z, -8.4e-299], y, If[LessEqual[z, 2.2e-269], x, If[LessEqual[z, 6e-192], y, If[LessEqual[z, 1.75e-133], x, If[LessEqual[z, 4.4e-66], y, If[LessEqual[z, 29000000000.0], x, N[(x * z), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 53.5%

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

      1. +-commutative 53.5%

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

      2. distribute-lft-in 53.5%

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

      3. *-rgt-identity 53.5%

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

   4. Applied egg-rr 53.5%

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

   5. Taylor expanded in z around inf 52.2%

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

      1. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if -1 < z < -1.80000000000000005e-124 or -1.39999999999999993e-247 < z < -8.40000000000000041e-299 or 2.19999999999999984e-269 < z < 5.9999999999999998e-192 or 1.75000000000000001e-133 < z < 4.4000000000000002e-66

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 46.1%

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

   3. Taylor expanded in z around 0 46.1%

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

   if -1.80000000000000005e-124 < z < -1.39999999999999993e-247 or -8.40000000000000041e-299 < z < 2.19999999999999984e-269 or 5.9999999999999998e-192 < z < 1.75000000000000001e-133 or 4.4000000000000002e-66 < z < 2.9e10

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 47.4%

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

   3. Taylor expanded in z around 0 47.0%

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

   if 2.9e10 < z

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. distribute-lft-in 62.1%

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

      3. *-rgt-identity 62.1%

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

   4. Applied egg-rr 62.1%

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

   5. Taylor expanded in z around inf 62.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-299}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.115 \lor \neg \left(z \leq 29000000000\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.115) (not (<= z 29000000000.0))) (* x (+ z 1.0)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.115) || !(z <= 29000000000.0)) {
		tmp = x * (z + 1.0);
	} 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 <= (-0.115d0)) .or. (.not. (z <= 29000000000.0d0))) then
        tmp = x * (z + 1.0d0)
    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 <= -0.115) || !(z <= 29000000000.0)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.115) or not (z <= 29000000000.0):
		tmp = x * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.115) || !(z <= 29000000000.0))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.115) || ~((z <= 29000000000.0)))
		tmp = x * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.115], N[Not[LessEqual[z, 29000000000.0]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.115000000000000005 or 2.9e10 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 57.3%

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

   if -0.115000000000000005 < z < 2.9e10

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 98.2%

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

      1. +-commutative 98.2%

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

   4. Simplified 98.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.115 \lor \neg \left(z \leq 29000000000\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 98.0% accurate, 0.8× 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. Taylor expanded in z around inf 98.4%

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

      1. +-commutative 98.4%

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

   4. Simplified 98.4%

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

   if -1 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 98.8%

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

      1. +-commutative 98.8%

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

   4. Simplified 98.8%

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

4. Final simplification 98.6%

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

Alternative 6: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* y z) (if (<= z 29000000000.0) (+ x y) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 29000000000.0) {
		tmp = x + 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 <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 29000000000.0d0) then
        tmp = x + 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 <= -1.0) {
		tmp = y * z;
	} else if (z <= 29000000000.0) {
		tmp = x + y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= 29000000000.0:
		tmp = x + y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 29000000000.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = y * z;
	elseif (z <= 29000000000.0)
		tmp = x + y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 29000000000.0], N[(x + y), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 53.5%

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

      1. +-commutative 53.5%

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

      2. distribute-lft-in 53.5%

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

      3. *-rgt-identity 53.5%

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

   4. Applied egg-rr 53.5%

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

   5. Taylor expanded in z around inf 52.2%

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

      1. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if -1 < z < 2.9e10

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 98.2%

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

      1. +-commutative 98.2%

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

   4. Simplified 98.2%

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

   if 2.9e10 < z

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. distribute-lft-in 62.1%

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

      3. *-rgt-identity 62.1%

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

   4. Applied egg-rr 62.1%

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

   5. Taylor expanded in z around inf 62.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 7: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e-59) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e-59) {
		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 <= (-1.1d-59)) 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 <= -1.1e-59) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.1e-59:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e-59)
		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 <= -1.1e-59)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e-59], 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 < -1.0999999999999999e-59

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 80.2%

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

   if -1.0999999999999999e-59 < x

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 57.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 8: 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. Final simplification 100.0%

   \[\leadsto \left(x + y\right) \cdot \left(z + 1\right) \]

Alternative 9: 31.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -9e-107) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e-107) {
		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 <= (-9d-107)) 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 <= -9e-107) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e-107:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e-107)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e-107)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e-107], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000032e-107

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 75.1%

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

   3. Taylor expanded in z around 0 40.2%

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

   if -9.00000000000000032e-107 < x

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 57.0%

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

   3. Taylor expanded in z around 0 32.5%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 26.5% 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. Taylor expanded in x around inf 54.6%

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

3. Taylor expanded in z around 0 29.0%

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

4. Final simplification 29.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))