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

Percentage Accurate: 99.9% → 99.9%

Time: 3.9s

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: 99.9% 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: 99.9% 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

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

   2. lift-*.f64 N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*l* N/A

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

   8. *-commutative N/A

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

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

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

   10. lower-fma.f64 N/A

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

   11. *-commutative N/A

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

   12. distribute-rgt-neg-in N/A

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

   13. lower-*.f64 N/A

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

   14. metadata-eval 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 50.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (-4.0d0) * (z * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 48.4

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

5. Applied rewrites 48.4%

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

6. Final simplification 48.4%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))