Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 10.3s

Alternatives: 7

Speedup: 1.0×

• 29.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))

C

double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * y) + z) * y) + t
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * y) + z) * y) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * y) + z) * y) + t)
end

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))

C

double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * y) + z) * y) + t
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * y) + z) * y) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * y) + z) * y) + t)
end

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return fma(fma(x, y, z), y, t);
}

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ t (* y (+ z (* x y)))))

C

double code(double x, double y, double z, double t) {
	return t + (y * (z + (x * y)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + (y * (z + (x * y)))
end function

Java

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

Python

def code(x, y, z, t):
	return t + (y * (z + (x * y)))

Julia

function code(x, y, z, t)
	return Float64(t + Float64(y * Float64(z + Float64(x * y))))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 3: 63.3% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* y (+ z (* x y))))

C

double code(double x, double y, double z, double t) {
	return y * (z + (x * y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * (z + (x * y))
end function

Java

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

Python

def code(x, y, z, t):
	return y * (z + (x * y))

Julia

function code(x, y, z, t)
	return Float64(y * Float64(z + Float64(x * y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Add Preprocessing

3. Taylor expanded in t around 0 65.4%

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

4. Final simplification 65.4%

   \[\leadsto y \cdot \left(z + x \cdot y\right) \]
5. Add Preprocessing

Alternative 4: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t + y \cdot \left(x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ t (* y (* x y))))

C

double code(double x, double y, double z, double t) {
	return t + (y * (x * y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + (y * (x * y))
end function

Java

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

Python

def code(x, y, z, t):
	return t + (y * (x * y))

Julia

function code(x, y, z, t)
	return Float64(t + Float64(y * Float64(x * y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Add Preprocessing

3. Taylor expanded in x around inf 75.4%

   \[\leadsto \color{blue}{x \cdot {y}^{2}} + t \]
4. Step-by-step derivation

   1. add-sqr-sqrt 51.5%

      \[\leadsto \color{blue}{\sqrt{x \cdot {y}^{2}} \cdot \sqrt{x \cdot {y}^{2}}} + t \]

   2. pow2 51.5%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot {y}^{2}}\right)}^{2}} + t \]

   3. *-commutative 51.5%

      \[\leadsto {\left(\sqrt{\color{blue}{{y}^{2} \cdot x}}\right)}^{2} + t \]

   4. sqrt-prod 41.6%

      \[\leadsto {\color{blue}{\left(\sqrt{{y}^{2}} \cdot \sqrt{x}\right)}}^{2} + t \]

   5. unpow2 41.6%

      \[\leadsto {\left(\sqrt{\color{blue}{y \cdot y}} \cdot \sqrt{x}\right)}^{2} + t \]

   6. sqrt-prod 20.4%

      \[\leadsto {\left(\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot \sqrt{x}\right)}^{2} + t \]

   7. add-sqr-sqrt 41.6%

      \[\leadsto {\left(\color{blue}{y} \cdot \sqrt{x}\right)}^{2} + t \]

5. Applied egg-rr 41.6%

   \[\leadsto \color{blue}{{\left(y \cdot \sqrt{x}\right)}^{2}} + t \]
6. Step-by-step derivation

   1. unpow2 41.6%

      \[\leadsto \color{blue}{\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)} + t \]

   2. *-commutative 41.6%

      \[\leadsto \left(y \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\sqrt{x} \cdot y\right)} + t \]

   3. associate-*r* 41.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \sqrt{x}\right) \cdot \sqrt{x}\right) \cdot y} + t \]

   4. associate-*r* 41.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)\right)} \cdot y + t \]

   5. add-sqr-sqrt 76.8%

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

   6. *-commutative 76.8%

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

7. Applied egg-rr 76.8%

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

8. Final simplification 76.8%

   \[\leadsto t + y \cdot \left(x \cdot y\right) \]
9. Add Preprocessing

Alternative 5: 39.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Add Preprocessing

3. Taylor expanded in t around 0 65.4%

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

   1. +-commutative 65.4%

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

   2. fma-udef 65.4%

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

   3. rem-cube-cbrt 64.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \mathsf{fma}\left(x, y, z\right)}\right)}^{3}} \]

5. Applied egg-rr 64.9%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \mathsf{fma}\left(x, y, z\right)}\right)}^{3}} \]

6. Taylor expanded in z around 0 23.3%

   \[\leadsto {\color{blue}{\left({\left(x \cdot {y}^{2}\right)}^{0.3333333333333333}\right)}}^{3} \]
7. Step-by-step derivation

   1. unpow1/3 40.8%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{x \cdot {y}^{2}}\right)}}^{3} \]

8. Simplified 40.8%

   \[\leadsto {\color{blue}{\left(\sqrt[3]{x \cdot {y}^{2}}\right)}}^{3} \]
9. Step-by-step derivation

   1. rem-cube-cbrt 40.9%

      \[\leadsto \color{blue}{x \cdot {y}^{2}} \]

   2. unpow2 40.9%

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

   3. associate-*l* 42.4%

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

10. Applied egg-rr 42.4%

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

11. Final simplification 42.4%

    \[\leadsto y \cdot \left(x \cdot y\right) \]
12. Add Preprocessing

Alternative 6: 66.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ t + y \cdot z \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ t (* y z)))

C

double code(double x, double y, double z, double t) {
	return t + (y * z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + (y * z)
end function

Java

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

Python

def code(x, y, z, t):
	return t + (y * z)

Julia

function code(x, y, z, t)
	return Float64(t + Float64(y * z))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 64.1%

   \[\leadsto \color{blue}{y \cdot z} + t \]

4. Final simplification 64.1%

   \[\leadsto t + y \cdot z \]
5. Add Preprocessing

Alternative 7: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 36.7%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 36.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024033 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))