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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 10

Speedup: 1.0×

• 20.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

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

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

   1. sub-neg 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+222}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+179} \lor \neg \left(z \leq 2.6 \cdot 10^{+229}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* y (- z))))
   (if (<= z -1e+222)
     t_0
     (if (<= z -3.15e+155)
       t_1
       (if (<= z -3.6e+62)
         t_0
         (if (<= z -200.0)
           t_1
           (if (<= z 1.0)
             (+ x y)
             (if (or (<= z 4.8e+179) (not (<= z 2.6e+229))) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * -z;
	double tmp;
	if (z <= -1e+222) {
		tmp = t_0;
	} else if (z <= -3.15e+155) {
		tmp = t_1;
	} else if (z <= -3.6e+62) {
		tmp = t_0;
	} else if (z <= -200.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 4.8e+179) || !(z <= 2.6e+229)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = y * -z
    if (z <= (-1d+222)) then
        tmp = t_0
    else if (z <= (-3.15d+155)) then
        tmp = t_1
    else if (z <= (-3.6d+62)) then
        tmp = t_0
    else if (z <= (-200.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 4.8d+179) .or. (.not. (z <= 2.6d+229))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * -z;
	double tmp;
	if (z <= -1e+222) {
		tmp = t_0;
	} else if (z <= -3.15e+155) {
		tmp = t_1;
	} else if (z <= -3.6e+62) {
		tmp = t_0;
	} else if (z <= -200.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 4.8e+179) || !(z <= 2.6e+229)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = y * -z
	tmp = 0
	if z <= -1e+222:
		tmp = t_0
	elif z <= -3.15e+155:
		tmp = t_1
	elif z <= -3.6e+62:
		tmp = t_0
	elif z <= -200.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 4.8e+179) or not (z <= 2.6e+229):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -1e+222)
		tmp = t_0;
	elseif (z <= -3.15e+155)
		tmp = t_1;
	elseif (z <= -3.6e+62)
		tmp = t_0;
	elseif (z <= -200.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 4.8e+179) || !(z <= 2.6e+229))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = y * -z;
	tmp = 0.0;
	if (z <= -1e+222)
		tmp = t_0;
	elseif (z <= -3.15e+155)
		tmp = t_1;
	elseif (z <= -3.6e+62)
		tmp = t_0;
	elseif (z <= -200.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 4.8e+179) || ~((z <= 2.6e+229)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -1e+222], t$95$0, If[LessEqual[z, -3.15e+155], t$95$1, If[LessEqual[z, -3.6e+62], t$95$0, If[LessEqual[z, -200.0], t$95$1, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 4.8e+179], N[Not[LessEqual[z, 2.6e+229]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e222 or -3.15e155 < z < -3.6e62 or 4.80000000000000025e179 < z < 2.6e229

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 67.3%

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

   6. Taylor expanded in z around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. neg-mul-1 67.3%

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

   8. Simplified 67.3%

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

   if -1e222 < z < -3.15e155 or -3.6e62 < z < -200 or 1 < z < 4.80000000000000025e179 or 2.6e229 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.3%

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

      1. sub-neg 80.3%

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

      2. +-commutative 80.3%

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

      3. associate-+l+ 80.3%

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

      4. sub-neg 80.3%

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

      5. +-commutative 80.3%

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

      6. remove-double-neg 80.3%

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

      7. mul-1-neg 80.3%

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

      8. distribute-lft-out 80.3%

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

      9. mul-1-neg 80.3%

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

      10. unsub-neg 80.3%

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

      11. *-commutative 80.3%

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

      12. *-commutative 80.3%

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

      13. associate-/l* 81.6%

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

      14. distribute-lft-out-- 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in z around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. associate-*r* 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. *-commutative 88.5%

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

      5. distribute-neg-in 88.5%

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

      6. metadata-eval 88.5%

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

      7. sub-neg 88.5%

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

   8. Simplified 88.5%

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

   9. Taylor expanded in x around 0 59.2%

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

       1. mul-1-neg 59.2%

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

       2. *-commutative 59.2%

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

       3. distribute-rgt-neg-in 59.2%

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

   11. Simplified 59.2%

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

   if -200 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -200:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+179} \lor \neg \left(z \leq 2.6 \cdot 10^{+229}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq -10:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 10:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 3 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+155} \lor \neg \left(1 - z \leq 5 \cdot 10^{+220}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))))
   (if (<= (- 1.0 z) -10.0)
     t_0
     (if (<= (- 1.0 z) 10.0)
       (+ x y)
       (if (<= (- 1.0 z) 3e+62)
         t_0
         (if (or (<= (- 1.0 z) 2e+155) (not (<= (- 1.0 z) 5e+220)))
           (* x (- z))
           (* y (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= -10.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 10.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 3e+62) {
		tmp = t_0;
	} else if (((1.0 - z) <= 2e+155) || !((1.0 - z) <= 5e+220)) {
		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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    if ((1.0d0 - z) <= (-10.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 10.0d0) then
        tmp = x + y
    else if ((1.0d0 - z) <= 3d+62) then
        tmp = t_0
    else if (((1.0d0 - z) <= 2d+155) .or. (.not. ((1.0d0 - z) <= 5d+220))) 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 t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= -10.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 10.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 3e+62) {
		tmp = t_0;
	} else if (((1.0 - z) <= 2e+155) || !((1.0 - z) <= 5e+220)) {
		tmp = x * -z;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	tmp = 0
	if (1.0 - z) <= -10.0:
		tmp = t_0
	elif (1.0 - z) <= 10.0:
		tmp = x + y
	elif (1.0 - z) <= 3e+62:
		tmp = t_0
	elif ((1.0 - z) <= 2e+155) or not ((1.0 - z) <= 5e+220):
		tmp = x * -z
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -10.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 10.0)
		tmp = Float64(x + y);
	elseif (Float64(1.0 - z) <= 3e+62)
		tmp = t_0;
	elseif ((Float64(1.0 - z) <= 2e+155) || !(Float64(1.0 - z) <= 5e+220))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	tmp = 0.0;
	if ((1.0 - z) <= -10.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 10.0)
		tmp = x + y;
	elseif ((1.0 - z) <= 3e+62)
		tmp = t_0;
	elseif (((1.0 - z) <= 2e+155) || ~(((1.0 - z) <= 5e+220)))
		tmp = x * -z;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -10.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 10.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 3e+62], t$95$0, If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+155], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+220]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -10 or 10 < (-.f64 #s(literal 1 binary64) z) < 3e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 55.9%

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

   if -10 < (-.f64 #s(literal 1 binary64) z) < 10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

   if 3e62 < (-.f64 #s(literal 1 binary64) z) < 2.00000000000000001e155 or 5.0000000000000002e220 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 65.3%

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

   6. Taylor expanded in z around inf 65.3%

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

      1. associate-*r* 65.3%

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

      2. neg-mul-1 65.3%

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

   8. Simplified 65.3%

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

   if 2.00000000000000001e155 < (-.f64 #s(literal 1 binary64) z) < 5.0000000000000002e220

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 90.2%

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

      1. sub-neg 90.2%

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

      2. +-commutative 90.2%

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

      3. associate-+l+ 90.2%

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

      4. sub-neg 90.2%

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

      5. +-commutative 90.2%

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

      6. remove-double-neg 90.2%

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

      7. mul-1-neg 90.2%

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

      8. distribute-lft-out 90.2%

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

      9. mul-1-neg 90.2%

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

      10. unsub-neg 90.2%

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

      11. *-commutative 90.2%

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

      12. *-commutative 90.2%

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

      13. associate-/l* 89.8%

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

      14. distribute-lft-out-- 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in z around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. associate-*r* 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. *-commutative 99.7%

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

      5. distribute-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 50.4%

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

       1. mul-1-neg 50.4%

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

       2. *-commutative 50.4%

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

       3. distribute-rgt-neg-in 50.4%

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

   11. Simplified 50.4%

       \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -10:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 10:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 3 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+155} \lor \neg \left(1 - z \leq 5 \cdot 10^{+220}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -10 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -10.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- x) y))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -10.0) || !((1.0 - z) <= 2.0)) {
		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 (((1.0d0 - z) <= (-10.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) 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 (((1.0 - z) <= -10.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-x - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -10.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-x - y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -10.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-x) - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -10.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-x - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -10.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -10 or 2 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.3%

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

      1. mul-1-neg 97.3%

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

      2. distribute-lft-neg-out 97.3%

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

      3. *-commutative 97.3%

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

      4. +-commutative 97.3%

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

   5. Simplified 97.3%

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

   if -10 < (-.f64 #s(literal 1 binary64) z) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -10 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-62}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-130}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e-62)
   (- x (* x z))
   (if (<= x -1.65e-130)
     (+ x y)
     (if (<= x -2.9e-148) (* x (- 1.0 z)) (* y (- 1.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-62) {
		tmp = x - (x * z);
	} else if (x <= -1.65e-130) {
		tmp = x + y;
	} else if (x <= -2.9e-148) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - 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 <= (-1d-62)) then
        tmp = x - (x * z)
    else if (x <= (-1.65d-130)) then
        tmp = x + y
    else if (x <= (-2.9d-148)) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-62) {
		tmp = x - (x * z);
	} else if (x <= -1.65e-130) {
		tmp = x + y;
	} else if (x <= -2.9e-148) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e-62:
		tmp = x - (x * z)
	elif x <= -1.65e-130:
		tmp = x + y
	elif x <= -2.9e-148:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e-62)
		tmp = Float64(x - Float64(x * z));
	elseif (x <= -1.65e-130)
		tmp = Float64(x + y);
	elseif (x <= -2.9e-148)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e-62)
		tmp = x - (x * z);
	elseif (x <= -1.65e-130)
		tmp = x + y;
	elseif (x <= -2.9e-148)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e-62], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.65e-130], N[(x + y), $MachinePrecision], If[LessEqual[x, -2.9e-148], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e-62

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

   7. Applied egg-rr 72.8%

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

   if -1e-62 < x < -1.6499999999999999e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -1.6499999999999999e-130 < x < -2.8999999999999998e-148

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 44.9%

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

      1. *-commutative 44.9%

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

   5. Simplified 44.9%

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

   if -2.8999999999999998e-148 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-62}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-130}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{-64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-130}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 z))))
   (if (<= x -5.9e-64)
     t_0
     (if (<= x -2e-130) (+ x y) (if (<= x -2.9e-148) t_0 (* y (- 1.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (x <= -5.9e-64) {
		tmp = t_0;
	} else if (x <= -2e-130) {
		tmp = x + y;
	} else if (x <= -2.9e-148) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - z)
    if (x <= (-5.9d-64)) then
        tmp = t_0
    else if (x <= (-2d-130)) then
        tmp = x + y
    else if (x <= (-2.9d-148)) then
        tmp = t_0
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (x <= -5.9e-64) {
		tmp = t_0;
	} else if (x <= -2e-130) {
		tmp = x + y;
	} else if (x <= -2.9e-148) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - z)
	tmp = 0
	if x <= -5.9e-64:
		tmp = t_0
	elif x <= -2e-130:
		tmp = x + y
	elif x <= -2.9e-148:
		tmp = t_0
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (x <= -5.9e-64)
		tmp = t_0;
	elseif (x <= -2e-130)
		tmp = Float64(x + y);
	elseif (x <= -2.9e-148)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - z);
	tmp = 0.0;
	if (x <= -5.9e-64)
		tmp = t_0;
	elseif (x <= -2e-130)
		tmp = x + y;
	elseif (x <= -2.9e-148)
		tmp = t_0;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.9e-64], t$95$0, If[LessEqual[x, -2e-130], N[(x + y), $MachinePrecision], If[LessEqual[x, -2.9e-148], t$95$0, N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.89999999999999995e-64 or -2.0000000000000002e-130 < x < -2.8999999999999998e-148

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -5.89999999999999995e-64 < x < -2.0000000000000002e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -2.8999999999999998e-148 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-130}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -140.0) (not (<= z 1.0))) (* y (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -140.0) || !(z <= 1.0)) {
		tmp = y * -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 <= (-140.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = y * -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 <= -140.0) || !(z <= 1.0)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -140.0) or not (z <= 1.0):
		tmp = y * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -140.0) || !(z <= 1.0))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -140.0) || ~((z <= 1.0)))
		tmp = y * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -140.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -140 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.4%

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

      1. sub-neg 84.4%

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

      2. +-commutative 84.4%

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

      3. associate-+l+ 84.4%

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

      4. sub-neg 84.4%

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

      5. +-commutative 84.4%

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

      6. remove-double-neg 84.4%

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

      7. mul-1-neg 84.4%

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

      8. distribute-lft-out 84.4%

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

      9. mul-1-neg 84.4%

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

      10. unsub-neg 84.4%

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

      11. *-commutative 84.4%

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

      12. *-commutative 84.4%

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

      13. associate-/l* 86.6%

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

      14. distribute-lft-out-- 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in z around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. associate-*r* 93.4%

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

      3. distribute-rgt-neg-in 93.4%

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

      4. *-commutative 93.4%

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

      5. distribute-neg-in 93.4%

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

      6. metadata-eval 93.4%

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

      7. sub-neg 93.4%

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

   8. Simplified 93.4%

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

   9. Taylor expanded in x around 0 50.6%

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

       1. mul-1-neg 50.6%

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

       2. *-commutative 50.6%

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

       3. distribute-rgt-neg-in 50.6%

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

   11. Simplified 50.6%

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

   if -140 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (- 1.0 z) (+ x y)))

C

double code(double x, double y, double z) {
	return (1.0 - 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 = (1.0d0 - z) * (x + y)
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Python

def code(x, y, z):
	return (1.0 - z) * (x + y)

Julia

function code(x, y, z)
	return Float64(Float64(1.0 - z) * Float64(x + y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 - z) * (x + y);
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 9: 51.5% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0 48.9%

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

   1. +-commutative 48.9%

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

5. Simplified 48.9%

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

6. Final simplification 48.9%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 10: 26.9% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 48.7%

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

   1. *-commutative 48.7%

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

5. Simplified 48.7%

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

6. Taylor expanded in z around 0 21.6%

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

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))