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

Percentage Accurate: 99.8% → 99.8%

Time: 10.3s

Alternatives: 5

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 99.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*r* N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x 3.0))))
   (if (<= t_0 -4e-25)
     (* x (* y 3.0))
     (if (<= t_0 2e+95) (- 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 <= -4e-25) {
		tmp = x * (y * 3.0);
	} else if (t_0 <= 2e+95) {
		tmp = -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 <= (-4d-25)) then
        tmp = x * (y * 3.0d0)
    else if (t_0 <= 2d+95) then
        tmp = -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 <= -4e-25) {
		tmp = x * (y * 3.0);
	} else if (t_0 <= 2e+95) {
		tmp = -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 <= -4e-25:
		tmp = x * (y * 3.0)
	elif t_0 <= 2e+95:
		tmp = -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 <= -4e-25)
		tmp = Float64(x * Float64(y * 3.0));
	elseif (t_0 <= 2e+95)
		tmp = Float64(-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 <= -4e-25)
		tmp = x * (y * 3.0);
	elseif (t_0 <= 2e+95)
		tmp = -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, -4e-25], N[(x * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+95], (-z), 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) < -4.00000000000000015e-25

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-neg-in N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-neg-in N/A

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

      8. metadata-eval N/A

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

      9. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

   if -4.00000000000000015e-25 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2.00000000000000004e95

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if 2.00000000000000004e95 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.8%

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

      1. +-rgt-identity N/A

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

      2. flip-+ N/A

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

      3. --rgt-identity N/A

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

      4. lower-/.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. swap-sqr N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. swap-sqr N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot \color{blue}{9}\right) \cdot \left(y \cdot y\right) - 0}{\left(x \cdot 3\right) \cdot y} - z \]

      17. lower-*.f64 11.7

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \color{blue}{\left(y \cdot y\right)} - 0}{\left(x \cdot 3\right) \cdot y} - z \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \left(y \cdot y\right) - 0}{\color{blue}{\left(x \cdot 3\right) \cdot y}} - z \]

      19. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \left(y \cdot y\right) - 0}{\color{blue}{\left(x \cdot 3\right)} \cdot y} - z \]

      20. associate-*l* N/A

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \left(y \cdot y\right) - 0}{\color{blue}{x \cdot \left(3 \cdot y\right)}} - z \]

      21. *-commutative N/A

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \left(y \cdot y\right) - 0}{\color{blue}{\left(3 \cdot y\right) \cdot x}} - z \]

      22. associate-*l* N/A

          \[\leadsto \frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \left(y \cdot y\right) - 0}{\color{blue}{3 \cdot \left(y \cdot x\right)}} - z \]

   4. Applied rewrites 11.7%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot x\right) \cdot 9\right) \cdot \left(y \cdot y\right) - 0}{3 \cdot \left(x \cdot y\right)}} - z \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 86.9

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

   7. Applied rewrites 86.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 3\right) \leq -4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 3\right) \leq 2 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \]
5. 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 2024229 
(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))