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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 6

Speedup: 1.0×

• 29.2% 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, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * (z + (x * 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 = (y * (z + (x * y))) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 90.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ t_2 := y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))) (t_2 (* y (fma y x z))))
   (if (<= t_1 -2e+36) t_2 (if (<= t_1 2e+160) (fma y z t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double t_2 = y * fma(y, x, z);
	double tmp;
	if (t_1 <= -2e+36) {
		tmp = t_2;
	} else if (t_1 <= 2e+160) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	t_2 = Float64(y * fma(y, x, z))
	tmp = 0.0
	if (t_1 <= -2e+36)
		tmp = t_2;
	elseif (t_1 <= 2e+160)
		tmp = fma(y, z, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y * x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+36], t$95$2, If[LessEqual[t$95$1, 2e+160], N[(y * z + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -2.00000000000000008e36 or 2.00000000000000001e160 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 91.9%

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

   if -2.00000000000000008e36 < (*.f64 (+.f64 (*.f64 x y) z) y) < 2.00000000000000001e160

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 87.9

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

   5. Applied rewrites 87.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z + x \cdot y\right) \leq -2 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \cdot \left(z + x \cdot y\right) \leq 2 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ t_2 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+221}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))) (t_2 (* y (* x y))))
   (if (<= t_1 -4e+246) t_2 (if (<= t_1 1e+221) (fma y z t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double t_2 = y * (x * y);
	double tmp;
	if (t_1 <= -4e+246) {
		tmp = t_2;
	} else if (t_1 <= 1e+221) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	t_2 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (t_1 <= -4e+246)
		tmp = t_2;
	elseif (t_1 <= 1e+221)
		tmp = fma(y, z, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+246], t$95$2, If[LessEqual[t$95$1, 1e+221], N[(y * z + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -4.00000000000000027e246 or 1e221 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if -4.00000000000000027e246 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1e221

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 83.1

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

   5. Applied rewrites 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z + x \cdot y\right) \leq -4 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot \left(z + x \cdot y\right) \leq 10^{+221}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e-42)
   (* y (fma y x z))
   (if (<= z 2.7e+103) (fma y (* x y) t) (fma y z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-42) {
		tmp = y * fma(y, x, z);
	} else if (z <= 2.7e+103) {
		tmp = fma(y, (x * y), t);
	} else {
		tmp = fma(y, z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e-42)
		tmp = Float64(y * fma(y, x, z));
	elseif (z <= 2.7e+103)
		tmp = fma(y, Float64(x * y), t);
	else
		tmp = fma(y, z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e-42], N[(y * N[(y * x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+103], N[(y * N[(x * y), $MachinePrecision] + t), $MachinePrecision], N[(y * z + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7000000000000002e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 83.0%

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

   if -3.7000000000000002e-42 < z < 2.69999999999999993e103

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if 2.69999999999999993e103 < 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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.6

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

   5. Applied rewrites 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 65.3

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

5. Applied rewrites 65.3%

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

Alternative 6: 29.5% accurate, 2.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = y * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 29.7

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

5. Applied rewrites 29.7%

   \[\leadsto \color{blue}{y \cdot z} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024233 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))