Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 6.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 78.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -50000000000000:\\ \;\;\;\;y \cdot \frac{3}{\frac{1}{x}}\\ \mathbf{elif}\;t\_0 \leq 20000000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x 3.0) y)))
   (if (<= t_0 -50000000000000.0)
     (* y (/ 3.0 (/ 1.0 x)))
     (if (<= t_0 20000000000000.0) (- 0.0 z) (* x (* 3.0 y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -50000000000000.0) {
		tmp = y * (3.0 / (1.0 / x));
	} else if (t_0 <= 20000000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 * 3.0d0) * y
    if (t_0 <= (-50000000000000.0d0)) then
        tmp = y * (3.0d0 / (1.0d0 / x))
    else if (t_0 <= 20000000000000.0d0) then
        tmp = 0.0d0 - z
    else
        tmp = x * (3.0d0 * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -50000000000000.0) {
		tmp = y * (3.0 / (1.0 / x));
	} else if (t_0 <= 20000000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (x * 3.0) * y
	tmp = 0
	if t_0 <= -50000000000000.0:
		tmp = y * (3.0 / (1.0 / x))
	elif t_0 <= 20000000000000.0:
		tmp = 0.0 - z
	else:
		tmp = x * (3.0 * y)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(x * 3.0) * y)
	tmp = 0.0
	if (t_0 <= -50000000000000.0)
		tmp = Float64(y * Float64(3.0 / Float64(1.0 / x)));
	elseif (t_0 <= 20000000000000.0)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(x * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (x * 3.0) * y;
	tmp = 0.0;
	if (t_0 <= -50000000000000.0)
		tmp = y * (3.0 / (1.0 / x));
	elseif (t_0 <= 20000000000000.0)
		tmp = 0.0 - z;
	else
		tmp = x * (3.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -50000000000000.0], N[(y * N[(3.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 20000000000000.0], N[(0.0 - z), $MachinePrecision], N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -5e13

   1. Initial program 99.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 79.1%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 79.1%

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

      1. associate-*r* N/A

         \[\leadsto \left(3 \cdot x\right) \cdot \color{blue}{y} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot x\right), \color{blue}{y}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot 3\right), y\right) \]

      4. *-lowering-*.f64 79.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 3\right), y\right) \]

   9. Applied egg-rr 79.0%

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

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot x\right), y\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{3}{1} \cdot x\right), y\right) \]

       3. associate-/r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{3}{\frac{1}{x}}\right), y\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(3, \left(\frac{1}{x}\right)\right), y\right) \]

       5. /-lowering-/.f64 78.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(3, \mathsf{/.f64}\left(1, x\right)\right), y\right) \]

   11. Applied egg-rr 78.9%

       \[\leadsto \color{blue}{\frac{3}{\frac{1}{x}}} \cdot y \]

   if -5e13 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2e13

   1. Initial program 99.9%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 84.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{0 - z} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 84.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   9. Applied egg-rr 84.1%

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

   if 2e13 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 81.4%

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

      1. *-commutative N/A

         \[\leadsto 3 \cdot \left(y \cdot \color{blue}{x}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(3 \cdot y\right) \cdot \color{blue}{x} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot y\right), \color{blue}{x}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot 3\right), x\right) \]

      5. *-lowering-*.f64 81.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, 3\right), x\right) \]

   9. Applied egg-rr 81.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 3\right) \cdot y \leq -50000000000000:\\ \;\;\;\;y \cdot \frac{3}{\frac{1}{x}}\\ \mathbf{elif}\;\left(x \cdot 3\right) \cdot y \leq 20000000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -50000000000000:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq 20000000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x 3.0) y)))
   (if (<= t_0 -50000000000000.0)
     (* 3.0 (* x y))
     (if (<= t_0 20000000000000.0) (- 0.0 z) (* x (* 3.0 y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -50000000000000.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= 20000000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 * 3.0d0) * y
    if (t_0 <= (-50000000000000.0d0)) then
        tmp = 3.0d0 * (x * y)
    else if (t_0 <= 20000000000000.0d0) then
        tmp = 0.0d0 - z
    else
        tmp = x * (3.0d0 * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -50000000000000.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= 20000000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (x * 3.0) * y
	tmp = 0
	if t_0 <= -50000000000000.0:
		tmp = 3.0 * (x * y)
	elif t_0 <= 20000000000000.0:
		tmp = 0.0 - z
	else:
		tmp = x * (3.0 * y)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(x * 3.0) * y)
	tmp = 0.0
	if (t_0 <= -50000000000000.0)
		tmp = Float64(3.0 * Float64(x * y));
	elseif (t_0 <= 20000000000000.0)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(x * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (x * 3.0) * y;
	tmp = 0.0;
	if (t_0 <= -50000000000000.0)
		tmp = 3.0 * (x * y);
	elseif (t_0 <= 20000000000000.0)
		tmp = 0.0 - z;
	else
		tmp = x * (3.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -50000000000000.0], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 20000000000000.0], N[(0.0 - z), $MachinePrecision], N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -5e13

   1. Initial program 99.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 79.1%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 79.1%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]

   if -5e13 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2e13

   1. Initial program 99.9%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 84.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{0 - z} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 84.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   9. Applied egg-rr 84.1%

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

   if 2e13 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 81.4%

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

      1. *-commutative N/A

         \[\leadsto 3 \cdot \left(y \cdot \color{blue}{x}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(3 \cdot y\right) \cdot \color{blue}{x} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot y\right), \color{blue}{x}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot 3\right), x\right) \]

      5. *-lowering-*.f64 81.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, 3\right), x\right) \]

   9. Applied egg-rr 81.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 3\right) \cdot y \leq -50000000000000:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\left(x \cdot 3\right) \cdot y \leq 20000000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -50000000000000:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq 20000000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x 3.0) y)))
   (if (<= t_0 -50000000000000.0)
     (* 3.0 (* x y))
     (if (<= t_0 20000000000000.0) (- 0.0 z) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -50000000000000.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= 20000000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 * 3.0d0) * y
    if (t_0 <= (-50000000000000.0d0)) then
        tmp = 3.0d0 * (x * y)
    else if (t_0 <= 20000000000000.0d0) then
        tmp = 0.0d0 - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -50000000000000.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= 20000000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (x * 3.0) * y
	tmp = 0
	if t_0 <= -50000000000000.0:
		tmp = 3.0 * (x * y)
	elif t_0 <= 20000000000000.0:
		tmp = 0.0 - z
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(x * 3.0) * y)
	tmp = 0.0
	if (t_0 <= -50000000000000.0)
		tmp = Float64(3.0 * Float64(x * y));
	elseif (t_0 <= 20000000000000.0)
		tmp = Float64(0.0 - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (x * 3.0) * y;
	tmp = 0.0;
	if (t_0 <= -50000000000000.0)
		tmp = 3.0 * (x * y);
	elseif (t_0 <= 20000000000000.0)
		tmp = 0.0 - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -50000000000000.0], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 20000000000000.0], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -5e13

   1. Initial program 99.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 79.1%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 79.1%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]

   if -5e13 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2e13

   1. Initial program 99.9%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 84.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{0 - z} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 84.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   9. Applied egg-rr 84.1%

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

   if 2e13 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 81.4%

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

      1. associate-*r* N/A

         \[\leadsto \left(3 \cdot x\right) \cdot \color{blue}{y} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot x\right), \color{blue}{y}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot 3\right), y\right) \]

      4. *-lowering-*.f64 81.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 3\right), y\right) \]

   9. Applied egg-rr 81.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 3\right) \cdot y \leq -50000000000000:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\left(x \cdot 3\right) \cdot y \leq 20000000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 3 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-86}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x y))))
   (if (<= x -2.4e+93) t_0 (if (<= x 2.55e-86) (- 0.0 z) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 3.0 * (x * y);
	double tmp;
	if (x <= -2.4e+93) {
		tmp = t_0;
	} else if (x <= 2.55e-86) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = 3.0d0 * (x * y)
    if (x <= (-2.4d+93)) then
        tmp = t_0
    else if (x <= 2.55d-86) then
        tmp = 0.0d0 - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 3.0 * (x * y);
	double tmp;
	if (x <= -2.4e+93) {
		tmp = t_0;
	} else if (x <= 2.55e-86) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 3.0 * (x * y)
	tmp = 0
	if x <= -2.4e+93:
		tmp = t_0
	elif x <= 2.55e-86:
		tmp = 0.0 - z
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(3.0 * Float64(x * y))
	tmp = 0.0
	if (x <= -2.4e+93)
		tmp = t_0;
	elseif (x <= 2.55e-86)
		tmp = Float64(0.0 - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 3.0 * (x * y);
	tmp = 0.0;
	if (x <= -2.4e+93)
		tmp = t_0;
	elseif (x <= 2.55e-86)
		tmp = 0.0 - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+93], t$95$0, If[LessEqual[x, 2.55e-86], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000001e93 or 2.55000000000000003e-86 < x

   1. Initial program 99.8%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 63.2%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]

   if -2.4000000000000001e93 < x < 2.55000000000000003e-86

   1. Initial program 99.9%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

      4. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 73.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   7. Simplified 73.9%

      \[\leadsto \color{blue}{0 - z} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 73.9%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   9. Applied egg-rr 73.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+93}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-86}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (3.0d0 * y)) - z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

   4. *-lowering-*.f64 99.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 7: 50.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 0 - z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- 0.0 z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 0.0 - z;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0 - z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return 0.0 - z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 0.0 - z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(0.0 - z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 0.0 - z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(0.0 - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

   4. *-lowering-*.f64 99.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot z} \]
6. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 56.8%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

7. Simplified 56.8%

   \[\leadsto \color{blue}{0 - z} \]
8. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-lowering-neg.f64 56.8%

      \[\leadsto \mathsf{neg.f64}\left(z\right) \]

9. Applied egg-rr 56.8%

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

10. Final simplification 56.8%

    \[\leadsto 0 - z \]
11. Add Preprocessing

Alternative 8: 2.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 z)

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return z
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot 3\right) \cdot y\right), \color{blue}{z}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(3 \cdot y\right)\right), z\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right), z\right) \]

   4. *-lowering-*.f64 99.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right), z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot z} \]
6. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 56.8%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

7. Simplified 56.8%

   \[\leadsto \color{blue}{0 - z} \]
8. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-lowering-neg.f64 56.8%

      \[\leadsto \mathsf{neg.f64}\left(z\right) \]

9. Applied egg-rr 56.8%

   \[\leadsto \color{blue}{-z} \]
10. Step-by-step derivation

    1. neg-mul-1 N/A

       \[\leadsto -1 \cdot \color{blue}{z} \]

    2. metadata-eval N/A

       \[\leadsto \frac{1}{-1} \cdot z \]

    3. associate-/r/ N/A

       \[\leadsto \frac{1}{\color{blue}{\frac{-1}{z}}} \]

    4. inv-pow N/A

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

    5. sqr-pow N/A

       \[\leadsto {\left(\frac{-1}{z}\right)}^{\left(\frac{-1}{2}\right)} \cdot \color{blue}{{\left(\frac{-1}{z}\right)}^{\left(\frac{-1}{2}\right)}} \]

    6. remove-double-neg N/A

       \[\leadsto {\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\color{blue}{-1}}{z}\right)}^{\left(\frac{-1}{2}\right)} \]

    7. neg-mul-1 N/A

       \[\leadsto {\left(-1 \cdot \left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\color{blue}{-1}}{z}\right)}^{\left(\frac{-1}{2}\right)} \]

    8. *-commutative N/A

       \[\leadsto {\left(\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right) \cdot -1\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\color{blue}{-1}}{z}\right)}^{\left(\frac{-1}{2}\right)} \]

    9. unpow-prod-down N/A

       \[\leadsto \left({\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot {-1}^{\left(\frac{-1}{2}\right)}\right) \cdot {\color{blue}{\left(\frac{-1}{z}\right)}}^{\left(\frac{-1}{2}\right)} \]

    10. associate-*l* N/A

        \[\leadsto {\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot \color{blue}{\left({-1}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{-1}{z}\right)}^{\left(\frac{-1}{2}\right)}\right)} \]

    11. unpow-prod-down N/A

        \[\leadsto {\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(-1 \cdot \frac{-1}{z}\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}} \]

    12. neg-mul-1 N/A

        \[\leadsto {\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

    13. sqr-pow N/A

        \[\leadsto {\left(\mathsf{neg}\left(\frac{-1}{z}\right)\right)}^{\color{blue}{-1}} \]

    14. inv-pow N/A

        \[\leadsto \frac{1}{\color{blue}{\mathsf{neg}\left(\frac{-1}{z}\right)}} \]

    15. distribute-neg-frac N/A

        \[\leadsto \frac{1}{\frac{\mathsf{neg}\left(-1\right)}{\color{blue}{z}}} \]

    16. metadata-eval N/A

        \[\leadsto \frac{1}{\frac{1}{z}} \]

    17. remove-double-div 2.2%

        \[\leadsto z \]

11. Applied egg-rr 2.2%

    \[\leadsto \color{blue}{z} \]
12. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (3.0d0 * y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* x (* 3 y)) z))

  (- (* (* x 3.0) y) z))