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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

Alternatives: 10

Speedup: 1.0×

• 21.5% 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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+215}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+194}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-304}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.75e+215)
   (* y z)
   (if (<= z -2.9e+194)
     (* x z)
     (if (<= z -1.35e+82)
       (* y z)
       (if (<= z -1.0)
         (* x z)
         (if (<= z -4.4e-158)
           y
           (if (<= z -8.2e-304) x (if (<= z 2.9) y (* x z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.75e+215) {
		tmp = y * z;
	} else if (z <= -2.9e+194) {
		tmp = x * z;
	} else if (z <= -1.35e+82) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -4.4e-158) {
		tmp = y;
	} else if (z <= -8.2e-304) {
		tmp = x;
	} else if (z <= 2.9) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.75d+215)) then
        tmp = y * z
    else if (z <= (-2.9d+194)) then
        tmp = x * z
    else if (z <= (-1.35d+82)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= (-4.4d-158)) then
        tmp = y
    else if (z <= (-8.2d-304)) then
        tmp = x
    else if (z <= 2.9d0) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.75e+215) {
		tmp = y * z;
	} else if (z <= -2.9e+194) {
		tmp = x * z;
	} else if (z <= -1.35e+82) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -4.4e-158) {
		tmp = y;
	} else if (z <= -8.2e-304) {
		tmp = x;
	} else if (z <= 2.9) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.75e+215:
		tmp = y * z
	elif z <= -2.9e+194:
		tmp = x * z
	elif z <= -1.35e+82:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= -4.4e-158:
		tmp = y
	elif z <= -8.2e-304:
		tmp = x
	elif z <= 2.9:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.75e+215)
		tmp = Float64(y * z);
	elseif (z <= -2.9e+194)
		tmp = Float64(x * z);
	elseif (z <= -1.35e+82)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= -4.4e-158)
		tmp = y;
	elseif (z <= -8.2e-304)
		tmp = x;
	elseif (z <= 2.9)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.75e+215)
		tmp = y * z;
	elseif (z <= -2.9e+194)
		tmp = x * z;
	elseif (z <= -1.35e+82)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= -4.4e-158)
		tmp = y;
	elseif (z <= -8.2e-304)
		tmp = x;
	elseif (z <= 2.9)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.75e+215], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.9e+194], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.35e+82], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.4e-158], y, If[LessEqual[z, -8.2e-304], x, If[LessEqual[z, 2.9], y, N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.74999999999999988e215 or -2.9000000000000001e194 < z < -1.35e82

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-lft-in 94.8%

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

      2. *-commutative 94.8%

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

   7. Applied egg-rr 94.8%

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

   8. Taylor expanded in y around inf 62.9%

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

      1. *-commutative 62.9%

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

   10. Simplified 62.9%

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

   if -1.74999999999999988e215 < z < -2.9000000000000001e194 or -1.35e82 < z < -1 or 2.89999999999999991 < 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 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

      1. distribute-lft-in 90.8%

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

      2. *-commutative 90.8%

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

   7. Applied egg-rr 90.8%

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

   8. Taylor expanded in y around 0 47.3%

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

      1. *-commutative 47.3%

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

   10. Simplified 47.3%

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

   if -1 < z < -4.4000000000000002e-158 or -8.20000000000000005e-304 < z < 2.89999999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 46.1%

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

   4. Taylor expanded in z around 0 44.9%

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

   if -4.4000000000000002e-158 < z < -8.20000000000000005e-304

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 45.4%

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

   6. Taylor expanded in z around 0 45.4%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+215}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+194}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-304}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+215}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+194}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-5} \lor \neg \left(z \leq 0.001\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e+215)
   (* y z)
   (if (<= z -7.8e+194)
     (* x z)
     (if (<= z -1.55e+82)
       (* y z)
       (if (or (<= z -2.2e-5) (not (<= z 0.001))) (* x (+ z 1.0)) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+215) {
		tmp = y * z;
	} else if (z <= -7.8e+194) {
		tmp = x * z;
	} else if (z <= -1.55e+82) {
		tmp = y * z;
	} else if ((z <= -2.2e-5) || !(z <= 0.001)) {
		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 <= (-3.1d+215)) then
        tmp = y * z
    else if (z <= (-7.8d+194)) then
        tmp = x * z
    else if (z <= (-1.55d+82)) then
        tmp = y * z
    else if ((z <= (-2.2d-5)) .or. (.not. (z <= 0.001d0))) 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 <= -3.1e+215) {
		tmp = y * z;
	} else if (z <= -7.8e+194) {
		tmp = x * z;
	} else if (z <= -1.55e+82) {
		tmp = y * z;
	} else if ((z <= -2.2e-5) || !(z <= 0.001)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e+215:
		tmp = y * z
	elif z <= -7.8e+194:
		tmp = x * z
	elif z <= -1.55e+82:
		tmp = y * z
	elif (z <= -2.2e-5) or not (z <= 0.001):
		tmp = x * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e+215)
		tmp = Float64(y * z);
	elseif (z <= -7.8e+194)
		tmp = Float64(x * z);
	elseif (z <= -1.55e+82)
		tmp = Float64(y * z);
	elseif ((z <= -2.2e-5) || !(z <= 0.001))
		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 <= -3.1e+215)
		tmp = y * z;
	elseif (z <= -7.8e+194)
		tmp = x * z;
	elseif (z <= -1.55e+82)
		tmp = y * z;
	elseif ((z <= -2.2e-5) || ~((z <= 0.001)))
		tmp = x * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e+215], N[(y * z), $MachinePrecision], If[LessEqual[z, -7.8e+194], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.55e+82], N[(y * z), $MachinePrecision], If[Or[LessEqual[z, -2.2e-5], N[Not[LessEqual[z, 0.001]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0999999999999999e215 or -7.80000000000000031e194 < z < -1.55000000000000016e82

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-lft-in 94.8%

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

      2. *-commutative 94.8%

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

   7. Applied egg-rr 94.8%

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

   8. Taylor expanded in y around inf 62.9%

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

      1. *-commutative 62.9%

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

   10. Simplified 62.9%

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

   if -3.0999999999999999e215 < z < -7.80000000000000031e194

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in y around 0 63.6%

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

      1. *-commutative 63.6%

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

   10. Simplified 63.6%

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

   if -1.55000000000000016e82 < z < -2.1999999999999999e-5 or 1e-3 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 46.8%

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

   if -2.1999999999999999e-5 < z < 1e-3

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.9%

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

      1. +-commutative 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+215}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+194}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-5} \lor \neg \left(z \leq 0.001\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+216}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+193}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+83}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+216)
   (* y z)
   (if (<= z -1.36e+193)
     (* x z)
     (if (<= z -1.5e+83)
       (* y z)
       (if (or (<= z -1.0) (not (<= z 5.0))) (* x z) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+216) {
		tmp = y * z;
	} else if (z <= -1.36e+193) {
		tmp = x * z;
	} else if (z <= -1.5e+83) {
		tmp = y * z;
	} else if ((z <= -1.0) || !(z <= 5.0)) {
		tmp = x * z;
	} 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 <= (-4d+216)) then
        tmp = y * z
    else if (z <= (-1.36d+193)) then
        tmp = x * z
    else if (z <= (-1.5d+83)) then
        tmp = y * z
    else if ((z <= (-1.0d0)) .or. (.not. (z <= 5.0d0))) then
        tmp = x * z
    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 <= -4e+216) {
		tmp = y * z;
	} else if (z <= -1.36e+193) {
		tmp = x * z;
	} else if (z <= -1.5e+83) {
		tmp = y * z;
	} else if ((z <= -1.0) || !(z <= 5.0)) {
		tmp = x * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+216:
		tmp = y * z
	elif z <= -1.36e+193:
		tmp = x * z
	elif z <= -1.5e+83:
		tmp = y * z
	elif (z <= -1.0) or not (z <= 5.0):
		tmp = x * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+216)
		tmp = Float64(y * z);
	elseif (z <= -1.36e+193)
		tmp = Float64(x * z);
	elseif (z <= -1.5e+83)
		tmp = Float64(y * z);
	elseif ((z <= -1.0) || !(z <= 5.0))
		tmp = Float64(x * z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e+216)
		tmp = y * z;
	elseif (z <= -1.36e+193)
		tmp = x * z;
	elseif (z <= -1.5e+83)
		tmp = y * z;
	elseif ((z <= -1.0) || ~((z <= 5.0)))
		tmp = x * z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+216], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.36e+193], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.5e+83], N[(y * z), $MachinePrecision], If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 5.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000001e216 or -1.35999999999999998e193 < z < -1.5e83

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-lft-in 94.8%

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

      2. *-commutative 94.8%

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

   7. Applied egg-rr 94.8%

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

   8. Taylor expanded in y around inf 62.9%

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

      1. *-commutative 62.9%

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

   10. Simplified 62.9%

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

   if -4.0000000000000001e216 < z < -1.35999999999999998e193 or -1.5e83 < z < -1 or 5 < 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 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

      1. distribute-lft-in 90.8%

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

      2. *-commutative 90.8%

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

   7. Applied egg-rr 90.8%

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

   8. Taylor expanded in y around 0 47.3%

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

      1. *-commutative 47.3%

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

   10. Simplified 47.3%

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

   if -1 < z < 5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+216}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+193}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+83}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* x z)
   (if (<= z -4e-158) y (if (<= z -1.4e-302) x (if (<= z 4.0) y (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -4e-158) {
		tmp = y;
	} else if (z <= -1.4e-302) {
		tmp = x;
	} else if (z <= 4.0) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= (-4d-158)) then
        tmp = y
    else if (z <= (-1.4d-302)) then
        tmp = x
    else if (z <= 4.0d0) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -4e-158) {
		tmp = y;
	} else if (z <= -1.4e-302) {
		tmp = x;
	} else if (z <= 4.0) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= -4e-158:
		tmp = y
	elif z <= -1.4e-302:
		tmp = x
	elif z <= 4.0:
		tmp = y
	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 <= -4e-158)
		tmp = y;
	elseif (z <= -1.4e-302)
		tmp = x;
	elseif (z <= 4.0)
		tmp = 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 = x * z;
	elseif (z <= -4e-158)
		tmp = y;
	elseif (z <= -1.4e-302)
		tmp = x;
	elseif (z <= 4.0)
		tmp = y;
	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, -4e-158], y, If[LessEqual[z, -1.4e-302], x, If[LessEqual[z, 4.0], y, N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 4 < 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 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

      1. distribute-lft-in 92.5%

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

      2. *-commutative 92.5%

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

   7. Applied egg-rr 92.5%

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

   8. Taylor expanded in y around 0 43.8%

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

      1. *-commutative 43.8%

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

   10. Simplified 43.8%

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

   if -1 < z < -4.00000000000000026e-158 or -1.4e-302 < z < 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 46.1%

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

   4. Taylor expanded in z around 0 44.9%

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

   if -4.00000000000000026e-158 < z < -1.4e-302

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 45.4%

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

   6. Taylor expanded in z around 0 45.4%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% 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 99.9%

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

   3. Taylor expanded in z around inf 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   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 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 98.0%

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

Alternative 7: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.25e-126) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-126) {
		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 <= 1.25d-126) 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 <= 1.25e-126) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.25e-126:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.25e-126)
		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 <= 1.25e-126)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.25e-126], 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 < 1.25000000000000001e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.8%

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

   if 1.25000000000000001e-126 < 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 67.7%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
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: 30.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 4.2e-124) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.2e-124) {
		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 <= 4.2d-124) 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 <= 4.2e-124) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.2e-124:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.2e-124)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.2e-124)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.2e-124], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 4.2000000000000002e-124

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 99.9%

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

      3. *-rgt-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 56.4%

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

   6. Taylor expanded in z around 0 30.4%

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

   if 4.2000000000000002e-124 < 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 67.4%

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

   4. Taylor expanded in z around 0 32.2%

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

Alternative 10: 26.2% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in y around 0 48.3%

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

6. Taylor expanded in z around 0 25.1%

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

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))