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

Percentage Accurate: 99.8% → 99.8%

Time: 7.8s

Alternatives: 7

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

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x * y) * 3.0) - 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) * 3.0d0) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 99.5%

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

3. Simplified 99.5%

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

   1. associate-*r* N/A

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

   2. *-commutative N/A

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

   3. associate-*r* N/A

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

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

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

   5. *-commutative N/A

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

   6. *-lowering-*.f64 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 78.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{y}{0.3333333333333333}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+19}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x 3.0))))
   (if (<= t_0 -5e+96)
     (* x (/ y 0.3333333333333333))
     (if (<= t_0 2e+19) (- 0.0 z) (* (* x y) 3.0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * 3.0);
	double tmp;
	if (t_0 <= -5e+96) {
		tmp = x * (y / 0.3333333333333333);
	} else if (t_0 <= 2e+19) {
		tmp = 0.0 - z;
	} else {
		tmp = (x * y) * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x * 3.0d0)
    if (t_0 <= (-5d+96)) then
        tmp = x * (y / 0.3333333333333333d0)
    else if (t_0 <= 2d+19) then
        tmp = 0.0d0 - z
    else
        tmp = (x * y) * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * 3.0);
	double tmp;
	if (t_0 <= -5e+96) {
		tmp = x * (y / 0.3333333333333333);
	} else if (t_0 <= 2e+19) {
		tmp = 0.0 - z;
	} else {
		tmp = (x * y) * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * 3.0)
	tmp = 0
	if t_0 <= -5e+96:
		tmp = x * (y / 0.3333333333333333)
	elif t_0 <= 2e+19:
		tmp = 0.0 - z
	else:
		tmp = (x * y) * 3.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * 3.0))
	tmp = 0.0
	if (t_0 <= -5e+96)
		tmp = Float64(x * Float64(y / 0.3333333333333333));
	elseif (t_0 <= 2e+19)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(Float64(x * y) * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * 3.0);
	tmp = 0.0;
	if (t_0 <= -5e+96)
		tmp = x * (y / 0.3333333333333333);
	elseif (t_0 <= 2e+19)
		tmp = 0.0 - z;
	else
		tmp = (x * y) * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+96], N[(x * N[(y / 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+19], N[(0.0 - z), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -5.0000000000000004e96

   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 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 86.4%

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

   7. Simplified 86.4%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 86.4%

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

   9. Applied egg-rr 86.4%

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. metadata-eval N/A

          \[\leadsto \left(x \cdot y\right) \cdot \frac{1}{\color{blue}{\frac{1}{3}}} \]

       4. div-inv N/A

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

       5. associate-/l* N/A

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

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

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

       7. /-lowering-/.f64 86.4%

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

   11. Applied egg-rr 86.4%

       \[\leadsto \color{blue}{x \cdot \frac{y}{0.3333333333333333}} \]

   if -5.0000000000000004e96 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2e19

   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 77.0%

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

   7. Simplified 77.0%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 77.0%

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

   9. Applied egg-rr 77.0%

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

   if 2e19 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   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 98.2%

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

   3. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   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 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 3\right) \leq -5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{y}{0.3333333333333333}\\ \mathbf{elif}\;y \cdot \left(x \cdot 3\right) \leq 2 \cdot 10^{+19}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot y\right) \cdot 3\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x y) 3.0)))
   (if (<= x -4.8e+58) t_0 (if (<= x 650.0) (- 0.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) * 3.0;
	double tmp;
	if (x <= -4.8e+58) {
		tmp = t_0;
	} else if (x <= 650.0) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * y) * 3.0d0
    if (x <= (-4.8d+58)) then
        tmp = t_0
    else if (x <= 650.0d0) then
        tmp = 0.0d0 - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * y) * 3.0;
	double tmp;
	if (x <= -4.8e+58) {
		tmp = t_0;
	} else if (x <= 650.0) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) * 3.0
	tmp = 0
	if x <= -4.8e+58:
		tmp = t_0
	elif x <= 650.0:
		tmp = 0.0 - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) * 3.0)
	tmp = 0.0
	if (x <= -4.8e+58)
		tmp = t_0;
	elseif (x <= 650.0)
		tmp = Float64(0.0 - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) * 3.0;
	tmp = 0.0;
	if (x <= -4.8e+58)
		tmp = t_0;
	elseif (x <= 650.0)
		tmp = 0.0 - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision]}, If[LessEqual[x, -4.8e+58], t$95$0, If[LessEqual[x, 650.0], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e58 or 650 < 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 74.2%

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

   7. Simplified 74.2%

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

   if -4.8e58 < x < 650

   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 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   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 73.5%

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

   7. Simplified 73.5%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 73.5%

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

   9. Applied egg-rr 73.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y * (x * 3.0)) - 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 = (y * (x * 3.0d0)) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (y * 3.0)) - 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 * 3.0d0)) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 6: 50.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ 0 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 0.0 z))

C

double code(double x, double y, double z) {
	return 0.0 - 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 = 0.0d0 - z
end function

Java

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

Python

def code(x, y, z):
	return 0.0 - z

Julia

function code(x, y, z)
	return Float64(0.0 - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0 - z;
end

Wolfram

code[x_, y_, z_] := N[(0.0 - z), $MachinePrecision]

Derivation

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 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
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 52.1%

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

7. Simplified 52.1%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 52.1%

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

9. Applied egg-rr 52.1%

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

10. Final simplification 52.1%

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

Alternative 7: 2.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

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 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
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 52.1%

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

7. Simplified 52.1%

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

   1. +-rgt-identity N/A

      \[\leadsto \left(0 - z\right) + \color{blue}{0} \]

   2. flip3-+ N/A

      \[\leadsto \frac{{\left(0 - z\right)}^{3} + {0}^{3}}{\color{blue}{\left(0 - z\right) \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)}} \]

   3. sqr-pow N/A

      \[\leadsto \frac{{\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)} + {0}^{3}}{\color{blue}{\left(0 - z\right)} \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   4. pow-prod-down N/A

      \[\leadsto \frac{{\left(\left(0 - z\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)} + {0}^{3}}{\color{blue}{\left(0 - z\right)} \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   5. sub0-neg N/A

      \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)} + {0}^{3}}{\left(0 - z\right) \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   6. sub0-neg N/A

      \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)} + {0}^{3}}{\left(0 - z\right) \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   7. sqr-neg N/A

      \[\leadsto \frac{{\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)} + {0}^{3}}{\left(\color{blue}{0} - z\right) \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   8. pow-prod-down N/A

      \[\leadsto \frac{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)} + {0}^{3}}{\color{blue}{\left(0 - z\right)} \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   9. sqr-pow N/A

      \[\leadsto \frac{{z}^{3} + {0}^{3}}{\color{blue}{\left(0 - z\right)} \cdot \left(0 - z\right) + \left(0 \cdot 0 - \left(0 - z\right) \cdot 0\right)} \]

   10. metadata-eval N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{\left(0 - z\right) \cdot \left(0 - z\right) + \left(0 - \color{blue}{\left(0 - z\right)} \cdot 0\right)} \]

   11. mul0-rgt N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{\left(0 - z\right) \cdot \left(0 - z\right) + \left(0 - 0\right)} \]

   12. metadata-eval N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{\left(0 - z\right) \cdot \left(0 - z\right) + 0} \]

   13. sub0-neg N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(0 - z\right) + 0} \]

   14. sub0-neg N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + 0} \]

   15. sqr-neg N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{z \cdot z + 0} \]

   16. metadata-eval N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{z \cdot z + \left(0 - \color{blue}{0}\right)} \]

   17. metadata-eval N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{z \cdot z + \left(0 \cdot 0 - 0\right)} \]

   18. mul0-lft N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{z \cdot z + \left(0 \cdot 0 - 0 \cdot \color{blue}{z}\right)} \]

   19. *-commutative N/A

       \[\leadsto \frac{{z}^{3} + {0}^{3}}{z \cdot z + \left(0 \cdot 0 - z \cdot \color{blue}{0}\right)} \]

   20. flip3-+ N/A

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

   21. +-rgt-identity 2.2%

       \[\leadsto z \]

9. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{z} \]
10. 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 2024138 
(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))