Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 2

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * 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 * 4.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((y * 4.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * 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 * 4.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((y * 4.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z \cdot -4, y, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* z -4.0) y x))

C

double code(double x, double y, double z) {
	return fma((z * -4.0), y, x);
}

Julia

function code(x, y, z)
	return fma(Float64(z * -4.0), y, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(z * -4.0), $MachinePrecision] * y + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. sub-neg N/A

      \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\left(y \cdot 4\right) \cdot z\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 4\right) \cdot z\right)\right) + x} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 4\right) \cdot z}\right)\right) + x \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 4\right)} \cdot z\right)\right) + x \]

   6. associate-*l* N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{y \cdot \left(4 \cdot z\right)}\right)\right) + x \]

   7. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(4 \cdot z\right) \cdot y}\right)\right) + x \]

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

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(4 \cdot z\right)\right) \cdot y} + x \]

   9. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(4 \cdot z\right), y, x\right)} \]

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

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, y, x\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, y, x\right) \]

   12. metadata-eval 100.0

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4} \cdot z, y, x\right) \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-4 \cdot z, y, x\right)} \]

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(z \cdot -4, y, x\right) \]
6. Add Preprocessing

Alternative 2: 50.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(y \cdot z\right) \cdot -4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (* y z) -4.0))

C

double code(double x, double y, double z) {
	return (y * z) * -4.0;
}

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 * z) * (-4.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (y * z) * -4.0;
}

Python

def code(x, y, z):
	return (y * z) * -4.0

Julia

function code(x, y, z)
	return Float64(Float64(y * z) * -4.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y * z) * -4.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(y * z), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -4} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -4} \]

   3. *-commutative N/A

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot -4 \]

   4. lower-*.f64 51.6

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot -4 \]

5. Applied rewrites 51.6%

   \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot -4} \]

6. Final simplification 51.6%

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

Reproduce

herbie shell --seed 2024257 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))