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

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 10

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. distribute-rgt-in N/A

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

   2. *-lft-identity N/A

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

   3. +-commutative N/A

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

   4. associate-+r+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(x + y\right) + y\right), \color{blue}{x}\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(x + y\right)\right), y\right), x\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\left(x + y\right) \cdot z\right), y\right), x\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x + y\right), z\right), y\right), x\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), y\right), x\right) \]

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 74.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z + 1\right)\\ \mathbf{if}\;z + 1 \leq -1 \cdot 10^{+155}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -100:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z + 1 \leq 1.00002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+162}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ z 1.0))))
   (if (<= (+ z 1.0) -1e+155)
     (* x z)
     (if (<= (+ z 1.0) -100.0)
       t_0
       (if (<= (+ z 1.0) 1.00002)
         (+ x y)
         (if (<= (+ z 1.0) 5e+16)
           t_0
           (if (<= (+ z 1.0) 5e+162) (* x z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z + 1.0);
	double tmp;
	if ((z + 1.0) <= -1e+155) {
		tmp = x * z;
	} else if ((z + 1.0) <= -100.0) {
		tmp = t_0;
	} else if ((z + 1.0) <= 1.00002) {
		tmp = x + y;
	} else if ((z + 1.0) <= 5e+16) {
		tmp = t_0;
	} else if ((z + 1.0) <= 5e+162) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z + 1.0d0)
    if ((z + 1.0d0) <= (-1d+155)) then
        tmp = x * z
    else if ((z + 1.0d0) <= (-100.0d0)) then
        tmp = t_0
    else if ((z + 1.0d0) <= 1.00002d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 5d+16) then
        tmp = t_0
    else if ((z + 1.0d0) <= 5d+162) then
        tmp = x * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z + 1.0);
	double tmp;
	if ((z + 1.0) <= -1e+155) {
		tmp = x * z;
	} else if ((z + 1.0) <= -100.0) {
		tmp = t_0;
	} else if ((z + 1.0) <= 1.00002) {
		tmp = x + y;
	} else if ((z + 1.0) <= 5e+16) {
		tmp = t_0;
	} else if ((z + 1.0) <= 5e+162) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z + 1.0)
	tmp = 0
	if (z + 1.0) <= -1e+155:
		tmp = x * z
	elif (z + 1.0) <= -100.0:
		tmp = t_0
	elif (z + 1.0) <= 1.00002:
		tmp = x + y
	elif (z + 1.0) <= 5e+16:
		tmp = t_0
	elif (z + 1.0) <= 5e+162:
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z + 1.0))
	tmp = 0.0
	if (Float64(z + 1.0) <= -1e+155)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= -100.0)
		tmp = t_0;
	elseif (Float64(z + 1.0) <= 1.00002)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 5e+16)
		tmp = t_0;
	elseif (Float64(z + 1.0) <= 5e+162)
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z + 1.0);
	tmp = 0.0;
	if ((z + 1.0) <= -1e+155)
		tmp = x * z;
	elseif ((z + 1.0) <= -100.0)
		tmp = t_0;
	elseif ((z + 1.0) <= 1.00002)
		tmp = x + y;
	elseif ((z + 1.0) <= 5e+16)
		tmp = t_0;
	elseif ((z + 1.0) <= 5e+162)
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z + 1.0), $MachinePrecision], -1e+155], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -100.0], t$95$0, If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.00002], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 5e+16], t$95$0, If[LessEqual[N[(z + 1.0), $MachinePrecision], 5e+162], N[(x * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -1.00000000000000001e155 or 5e16 < (+.f64 z #s(literal 1 binary64)) < 4.9999999999999997e162

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 56.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 56.3%

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

   if -1.00000000000000001e155 < (+.f64 z #s(literal 1 binary64)) < -100 or 1.00001999999999991 < (+.f64 z #s(literal 1 binary64)) < 5e16 or 4.9999999999999997e162 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 53.5%

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

   if -100 < (+.f64 z #s(literal 1 binary64)) < 1.00001999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 99.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -1 \cdot 10^{+155}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -100:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z + 1 \leq 1.00002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+162}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+150}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-125}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+164}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+150)
   (* x z)
   (if (<= z -8e-16)
     (* y z)
     (if (<= z -9e-125)
       y
       (if (<= z 1.7e-119)
         x
         (if (<= z 4.5e+16) y (if (<= z 3.4e+164) (* x z) (* y z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+150) {
		tmp = x * z;
	} else if (z <= -8e-16) {
		tmp = y * z;
	} else if (z <= -9e-125) {
		tmp = y;
	} else if (z <= 1.7e-119) {
		tmp = x;
	} else if (z <= 4.5e+16) {
		tmp = y;
	} else if (z <= 3.4e+164) {
		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 <= (-4d+150)) then
        tmp = x * z
    else if (z <= (-8d-16)) then
        tmp = y * z
    else if (z <= (-9d-125)) then
        tmp = y
    else if (z <= 1.7d-119) then
        tmp = x
    else if (z <= 4.5d+16) then
        tmp = y
    else if (z <= 3.4d+164) 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 <= -4e+150) {
		tmp = x * z;
	} else if (z <= -8e-16) {
		tmp = y * z;
	} else if (z <= -9e-125) {
		tmp = y;
	} else if (z <= 1.7e-119) {
		tmp = x;
	} else if (z <= 4.5e+16) {
		tmp = y;
	} else if (z <= 3.4e+164) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+150:
		tmp = x * z
	elif z <= -8e-16:
		tmp = y * z
	elif z <= -9e-125:
		tmp = y
	elif z <= 1.7e-119:
		tmp = x
	elif z <= 4.5e+16:
		tmp = y
	elif z <= 3.4e+164:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+150)
		tmp = Float64(x * z);
	elseif (z <= -8e-16)
		tmp = Float64(y * z);
	elseif (z <= -9e-125)
		tmp = y;
	elseif (z <= 1.7e-119)
		tmp = x;
	elseif (z <= 4.5e+16)
		tmp = y;
	elseif (z <= 3.4e+164)
		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 <= -4e+150)
		tmp = x * z;
	elseif (z <= -8e-16)
		tmp = y * z;
	elseif (z <= -9e-125)
		tmp = y;
	elseif (z <= 1.7e-119)
		tmp = x;
	elseif (z <= 4.5e+16)
		tmp = y;
	elseif (z <= 3.4e+164)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+150], N[(x * z), $MachinePrecision], If[LessEqual[z, -8e-16], N[(y * z), $MachinePrecision], If[LessEqual[z, -9e-125], y, If[LessEqual[z, 1.7e-119], x, If[LessEqual[z, 4.5e+16], y, If[LessEqual[z, 3.4e+164], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999992e150 or 4.5e16 < z < 3.4000000000000001e164

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 56.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 56.3%

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

   if -3.99999999999999992e150 < z < -7.9999999999999998e-16 or 3.4000000000000001e164 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 95.0%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 52.1%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   8. Simplified 52.1%

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

   if -7.9999999999999998e-16 < z < -9.00000000000000024e-125 or 1.70000000000000012e-119 < z < 4.5e16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 89.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 40.0%

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

   if -9.00000000000000024e-125 < z < 1.70000000000000012e-119

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 58.9%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+150}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-125}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+164}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 10^{+164}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e+150)
   (* x z)
   (if (<= z -1.0)
     (* y z)
     (if (<= z 4.5e+16) (+ x y) (if (<= z 1e+164) (* x z) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e+150) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 4.5e+16) {
		tmp = x + y;
	} else if (z <= 1e+164) {
		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 <= (-1.2d+150)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 4.5d+16) then
        tmp = x + y
    else if (z <= 1d+164) 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 <= -1.2e+150) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 4.5e+16) {
		tmp = x + y;
	} else if (z <= 1e+164) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e+150:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 4.5e+16:
		tmp = x + y
	elif z <= 1e+164:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e+150)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 4.5e+16)
		tmp = Float64(x + y);
	elseif (z <= 1e+164)
		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 <= -1.2e+150)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 4.5e+16)
		tmp = x + y;
	elseif (z <= 1e+164)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e+150], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 4.5e+16], N[(x + y), $MachinePrecision], If[LessEqual[z, 1e+164], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000001e150 or 4.5e16 < z < 1e164

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 56.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 56.3%

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

   if -1.20000000000000001e150 < z < -1 or 1e164 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 98.2%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   8. Simplified 53.7%

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

   if -1 < z < 4.5e16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 95.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 95.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 10^{+164}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-125}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8e-16)
   (* y z)
   (if (<= z -9e-125) y (if (<= z 4.5e-116) x (if (<= z 1.0) y (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8e-16) {
		tmp = y * z;
	} else if (z <= -9e-125) {
		tmp = y;
	} else if (z <= 4.5e-116) {
		tmp = x;
	} else if (z <= 1.0) {
		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 <= (-8d-16)) then
        tmp = y * z
    else if (z <= (-9d-125)) then
        tmp = y
    else if (z <= 4.5d-116) then
        tmp = x
    else if (z <= 1.0d0) 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 <= -8e-16) {
		tmp = y * z;
	} else if (z <= -9e-125) {
		tmp = y;
	} else if (z <= 4.5e-116) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8e-16:
		tmp = y * z
	elif z <= -9e-125:
		tmp = y
	elif z <= 4.5e-116:
		tmp = x
	elif z <= 1.0:
		tmp = y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8e-16)
		tmp = Float64(y * z);
	elseif (z <= -9e-125)
		tmp = y;
	elseif (z <= 4.5e-116)
		tmp = x;
	elseif (z <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8e-16)
		tmp = y * z;
	elseif (z <= -9e-125)
		tmp = y;
	elseif (z <= 4.5e-116)
		tmp = x;
	elseif (z <= 1.0)
		tmp = y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8e-16], N[(y * z), $MachinePrecision], If[LessEqual[z, -9e-125], y, If[LessEqual[z, 4.5e-116], x, If[LessEqual[z, 1.0], y, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999998e-16 or 1 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 96.1%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   8. Simplified 50.5%

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

   if -7.9999999999999998e-16 < z < -9.00000000000000024e-125 or 4.50000000000000012e-116 < 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

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 98.7%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 98.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 43.8%

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

   if -9.00000000000000024e-125 < z < 4.50000000000000012e-116

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 58.9%

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

Alternative 6: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-228) (* x (+ z 1.0)) (+ y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-228) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (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 ((x + y) <= (-1d-228)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-228) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-228:
		tmp = x * (z + 1.0)
	else:
		tmp = y + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-228)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-228)
		tmp = x * (z + 1.0);
	else
		tmp = y + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-228], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000003e-228

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 62.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 62.0%

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

   if -1.00000000000000003e-228 < (+.f64 x 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

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.6%

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

         \[\leadsto y \cdot z + y \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 52.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, z\right), y\right) \]

   7. Applied egg-rr 52.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-228) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-228) {
		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 + y) <= (-1d-228)) 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 + y) <= -1e-228) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-228:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-228)
		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 + y) <= -1e-228)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-228], 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 (+.f64 x y) < -1.00000000000000003e-228

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 62.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 62.0%

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

   if -1.00000000000000003e-228 < (+.f64 x 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

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing
3. Add Preprocessing

Alternative 9: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 4.5e-131) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.5e-131) {
		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 <= 4.5d-131) 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 <= 4.5e-131) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.5e-131:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.5e-131)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.5e-131)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.5e-131], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 4.5000000000000002e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 57.6%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 38.6%

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

   if 4.5000000000000002e-131 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 47.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 47.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 31.0%

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

Alternative 10: 26.1% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 54.3%

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

5. Simplified 54.3%

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

6. Taylor expanded in y around 0

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

8. Simplified 32.1%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))