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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 9

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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, 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 2: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -5.1e+112)
     t_0
     (if (<= z -1.05e+73)
       (* z (- y))
       (if (<= z -7.0) t_0 (if (<= z 9e-9) (+ x y) (* y (- 1.0 z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -5.1e+112) {
		tmp = t_0;
	} else if (z <= -1.05e+73) {
		tmp = z * -y;
	} else if (z <= -7.0) {
		tmp = t_0;
	} else if (z <= 9e-9) {
		tmp = x + y;
	} 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 * -z
    if (z <= (-5.1d+112)) then
        tmp = t_0
    else if (z <= (-1.05d+73)) then
        tmp = z * -y
    else if (z <= (-7.0d0)) then
        tmp = t_0
    else if (z <= 9d-9) then
        tmp = x + y
    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 * -z;
	double tmp;
	if (z <= -5.1e+112) {
		tmp = t_0;
	} else if (z <= -1.05e+73) {
		tmp = z * -y;
	} else if (z <= -7.0) {
		tmp = t_0;
	} else if (z <= 9e-9) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -5.1e+112:
		tmp = t_0
	elif z <= -1.05e+73:
		tmp = z * -y
	elif z <= -7.0:
		tmp = t_0
	elif z <= 9e-9:
		tmp = x + y
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -5.1e+112)
		tmp = t_0;
	elseif (z <= -1.05e+73)
		tmp = Float64(z * Float64(-y));
	elseif (z <= -7.0)
		tmp = t_0;
	elseif (z <= 9e-9)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -5.1e+112)
		tmp = t_0;
	elseif (z <= -1.05e+73)
		tmp = z * -y;
	elseif (z <= -7.0)
		tmp = t_0;
	elseif (z <= 9e-9)
		tmp = x + y;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -5.1e+112], t$95$0, If[LessEqual[z, -1.05e+73], N[(z * (-y)), $MachinePrecision], If[LessEqual[z, -7.0], t$95$0, If[LessEqual[z, 9e-9], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.10000000000000011e112 or -1.0500000000000001e73 < z < -7

   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 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 50.8%

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

   6. Taylor expanded in z around inf 49.4%

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

      1. associate-*r* 49.4%

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

      2. neg-mul-1 49.4%

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

   8. Simplified 49.4%

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

   if -5.10000000000000011e112 < z < -1.0500000000000001e73

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.5%

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

      1. sub-neg 79.5%

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

      2. +-commutative 79.5%

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

      3. associate-+l+ 79.5%

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

      4. sub-neg 79.5%

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

      5. +-commutative 79.5%

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

      6. remove-double-neg 79.5%

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

      7. mul-1-neg 79.5%

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

      8. distribute-lft-out 79.5%

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

      9. distribute-rgt-neg-in 79.5%

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

      10. *-commutative 79.5%

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

      11. distribute-rgt-neg-in 79.5%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in z around inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. distribute-rgt-neg-in 79.3%

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

      3. distribute-rgt-neg-out 79.3%

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

      4. mul-1-neg 79.3%

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

      5. distribute-lft-in 79.3%

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

      6. metadata-eval 79.3%

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

      7. mul-1-neg 79.3%

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

      8. unsub-neg 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in y around inf 25.3%

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

       1. mul-1-neg 25.3%

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

       2. *-commutative 25.3%

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

       3. distribute-rgt-neg-in 25.3%

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

   11. Simplified 25.3%

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

   if -7 < z < 8.99999999999999953e-9

   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 8.99999999999999953e-9 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 45.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -7:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -3.45 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* z (- y))))
   (if (<= z -3.45e+112)
     t_0
     (if (<= z -3.8e+72)
       t_1
       (if (<= z -7.5) t_0 (if (<= z 1.0) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = z * -y;
	double tmp;
	if (z <= -3.45e+112) {
		tmp = t_0;
	} else if (z <= -3.8e+72) {
		tmp = t_1;
	} else if (z <= -7.5) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	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 = z * -y
    if (z <= (-3.45d+112)) then
        tmp = t_0
    else if (z <= (-3.8d+72)) then
        tmp = t_1
    else if (z <= (-7.5d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else
        tmp = t_1
    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 = z * -y;
	double tmp;
	if (z <= -3.45e+112) {
		tmp = t_0;
	} else if (z <= -3.8e+72) {
		tmp = t_1;
	} else if (z <= -7.5) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = z * -y
	tmp = 0
	if z <= -3.45e+112:
		tmp = t_0
	elif z <= -3.8e+72:
		tmp = t_1
	elif z <= -7.5:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (z <= -3.45e+112)
		tmp = t_0;
	elseif (z <= -3.8e+72)
		tmp = t_1;
	elseif (z <= -7.5)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = z * -y;
	tmp = 0.0;
	if (z <= -3.45e+112)
		tmp = t_0;
	elseif (z <= -3.8e+72)
		tmp = t_1;
	elseif (z <= -7.5)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[z, -3.45e+112], t$95$0, If[LessEqual[z, -3.8e+72], t$95$1, If[LessEqual[z, -7.5], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.45e112 or -3.80000000000000006e72 < z < -7.5

   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 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 50.8%

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

   6. Taylor expanded in z around inf 49.4%

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

      1. associate-*r* 49.4%

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

      2. neg-mul-1 49.4%

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

   8. Simplified 49.4%

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

   if -3.45e112 < z < -3.80000000000000006e72 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. sub-neg 84.6%

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

      2. +-commutative 84.6%

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

      3. associate-+l+ 84.6%

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

      4. sub-neg 84.6%

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

      5. +-commutative 84.6%

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

      6. remove-double-neg 84.6%

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

      7. mul-1-neg 84.6%

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

      8. distribute-lft-out 84.6%

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

      9. distribute-rgt-neg-in 84.6%

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

      10. *-commutative 84.6%

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

      11. distribute-rgt-neg-in 84.6%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-in 87.3%

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

      3. distribute-rgt-neg-out 87.3%

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

      4. mul-1-neg 87.3%

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

      5. distribute-lft-in 87.3%

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

      6. metadata-eval 87.3%

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

      7. mul-1-neg 87.3%

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

      8. unsub-neg 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in y around inf 45.3%

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

       1. mul-1-neg 45.3%

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

       2. *-commutative 45.3%

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

       3. distribute-rgt-neg-in 45.3%

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

   11. Simplified 45.3%

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

   if -7.5 < 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 95.8%

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

      1. +-commutative 95.8%

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

   5. Simplified 95.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -7.5:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -5 \cdot 10^{+22} \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -5e+22) (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) <= -5e+22) || !((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) <= (-5d+22)) .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) <= -5e+22) || !((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) <= -5e+22) 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) <= -5e+22) || !(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) <= -5e+22) || ~(((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], -5e+22], 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) < -4.9999999999999996e22 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 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-lft-neg-out 98.7%

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

      3. *-commutative 98.7%

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

      4. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   if -4.9999999999999996e22 < (-.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 95.8%

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

      1. +-commutative 95.8%

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

   5. Simplified 95.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5 \cdot 10^{+22} \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -49 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -49.0) (not (<= z 1.0))) (* z (- y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -49.0) || !(z <= 1.0)) {
		tmp = z * -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 <= (-49.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -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 <= -49.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -49.0) or not (z <= 1.0):
		tmp = z * -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -49.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -49.0) || ~((z <= 1.0)))
		tmp = z * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -49.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -49 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.8%

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

      1. sub-neg 83.8%

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

      2. +-commutative 83.8%

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

      3. associate-+l+ 83.8%

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

      4. sub-neg 83.8%

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

      5. +-commutative 83.8%

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

      6. remove-double-neg 83.8%

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

      7. mul-1-neg 83.8%

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

      8. distribute-lft-out 83.8%

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

      9. distribute-rgt-neg-in 83.8%

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

      10. *-commutative 83.8%

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

      11. distribute-rgt-neg-in 83.8%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in z around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-rgt-neg-in 85.4%

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

      3. distribute-rgt-neg-out 85.4%

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

      4. mul-1-neg 85.4%

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

      5. distribute-lft-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. mul-1-neg 85.4%

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

      8. unsub-neg 85.4%

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

   8. Simplified 85.4%

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

   9. Taylor expanded in y around inf 49.3%

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

       1. mul-1-neg 49.3%

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

       2. *-commutative 49.3%

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

       3. distribute-rgt-neg-in 49.3%

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

   11. Simplified 49.3%

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

   if -49 < 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 95.1%

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

      1. +-commutative 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -49 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.4e-5) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-5) {
		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 (y <= 2.4d-5) 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 (y <= 2.4e-5) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.4e-5:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.4e-5)
		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 (y <= 2.4e-5)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.4e-5], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4000000000000001e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   if 2.4000000000000001e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 32.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.65e-5) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.65e-5) {
		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 <= 2.65d-5) 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 <= 2.65e-5) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.65e-5:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.65e-5)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.65e-5)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.65e-5], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.65e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in z around 0 30.0%

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

   if 2.65e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.1%

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

   4. Taylor expanded in z around 0 37.2%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% 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 49.2%

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

   1. +-commutative 49.2%

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

5. Simplified 49.2%

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

6. Final simplification 49.2%

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

Alternative 9: 26.9% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 54.6%

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

   1. *-commutative 54.6%

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

5. Simplified 54.6%

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

6. Taylor expanded in z around 0 25.7%

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

7. Final simplification 25.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024072 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))