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

Percentage Accurate: 99.9% → 99.9%

Time: 7.5s

Alternatives: 5

Speedup: 1.0×

• 29.7% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. fma-define 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+37} \lor \neg \left(z \leq 1.4 \cdot 10^{+86}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e+37) (not (<= z 1.4e+86)))
   (+ t (* y z))
   (+ t (* y (* y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e+37) || !(z <= 1.4e+86)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (y * x));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-9.2d+37)) .or. (.not. (z <= 1.4d+86))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (y * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e+37) || !(z <= 1.4e+86)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (y * x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e+37) or not (z <= 1.4e+86):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (y * x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e+37) || !(z <= 1.4e+86))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(y * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e+37) || ~((z <= 1.4e+86)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e+37], N[Not[LessEqual[z, 1.4e+86]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000001e37 or 1.40000000000000002e86 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.1%

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

   if -9.2000000000000001e37 < z < 1.40000000000000002e86

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.9%

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

      1. *-commutative 94.9%

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

   5. Simplified 94.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot y + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+37} \lor \neg \left(z \leq 1.4 \cdot 10^{+86}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (y * x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 4: 66.0% 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 65.1%

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

4. Final simplification 65.1%

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

Alternative 5: 39.4% 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. Step-by-step derivation

   1. *-commutative 99.9%

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

   2. fma-define 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 32.7%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))