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

Percentage Accurate: 99.9% → 99.9%

Time: 3.8s

Alternatives: 5

Speedup: 1.0×

• 29.3% 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

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

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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+98} \lor \neg \left(t\_1 \leq 10^{+141}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (or (<= t_1 -2e+98) (not (<= t_1 1e+141)))
     (* (fma y x z) y)
     (fma z y t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if ((t_1 <= -2e+98) || !(t_1 <= 1e+141)) {
		tmp = fma(y, x, z) * y;
	} else {
		tmp = fma(z, y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if ((t_1 <= -2e+98) || !(t_1 <= 1e+141))
		tmp = Float64(fma(y, x, z) * y);
	else
		tmp = fma(z, y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+98], N[Not[LessEqual[t$95$1, 1e+141]], $MachinePrecision]], N[(N[(y * x + z), $MachinePrecision] * y), $MachinePrecision], N[(z * y + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -2e98 or 1.00000000000000002e141 < (*.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

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

         \[\leadsto {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{-1 \cdot \left(x + \frac{z}{y}\right)}\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)}\right)\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)} \]

      5. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - {y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)} \]

      6. unsub-neg N/A

         \[\leadsto \color{blue}{0 + \left(\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right)} \]

      7. mul0-rgt N/A

         \[\leadsto \color{blue}{y \cdot 0} + \left(\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto y \cdot 0 + \color{blue}{{y}^{2} \cdot \left(\mathsf{neg}\left(\left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right)} \]

      9. distribute-lft-out N/A

         \[\leadsto y \cdot 0 + {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{-1 \cdot \left(x + \frac{z}{y}\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto y \cdot 0 + {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\left(x + \frac{z}{y}\right)\right)\right)}\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto y \cdot 0 + {y}^{2} \cdot \color{blue}{\left(x + \frac{z}{y}\right)} \]

      12. unpow2 N/A

          \[\leadsto y \cdot 0 + \color{blue}{\left(y \cdot y\right)} \cdot \left(x + \frac{z}{y}\right) \]

      13. associate-*l* N/A

          \[\leadsto y \cdot 0 + \color{blue}{y \cdot \left(y \cdot \left(x + \frac{z}{y}\right)\right)} \]

      14. distribute-lft-in N/A

          \[\leadsto \color{blue}{y \cdot \left(0 + y \cdot \left(x + \frac{z}{y}\right)\right)} \]

      15. +-lft-identity N/A

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

      16. distribute-rgt-in N/A

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

      17. cancel-sign-sub N/A

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

      18. mul-1-neg N/A

          \[\leadsto y \cdot \left(x \cdot y - \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \cdot y\right) \]

   5. Applied rewrites 94.7%

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

   if -2e98 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1.00000000000000002e141

   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. *-commutative N/A

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

      3. lower-fma.f64 94.1

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

   5. Applied rewrites 94.1%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z\right) \cdot y \leq -2 \cdot 10^{+98} \lor \neg \left(\left(x \cdot y + z\right) \cdot y \leq 10^{+141}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+191} \lor \neg \left(t\_1 \leq 10^{+262}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (or (<= t_1 -5e+191) (not (<= t_1 1e+262))) (* (* x y) y) (fma z y t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if ((t_1 <= -5e+191) || !(t_1 <= 1e+262)) {
		tmp = (x * y) * y;
	} else {
		tmp = fma(z, y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if ((t_1 <= -5e+191) || !(t_1 <= 1e+262))
		tmp = Float64(Float64(x * y) * y);
	else
		tmp = fma(z, y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+191], N[Not[LessEqual[t$95$1, 1e+262]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision], N[(z * y + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -5.0000000000000002e191 or 1e262 < (*.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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 81.9

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

   5. Applied rewrites 81.9%

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

   7. Applied rewrites 84.0%

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

   if -5.0000000000000002e191 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1e262

   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. *-commutative N/A

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

      3. lower-fma.f64 87.8

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

   5. Applied rewrites 87.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z\right) \cdot y \leq -5 \cdot 10^{+191} \lor \neg \left(\left(x \cdot y + z\right) \cdot y \leq 10^{+262}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 67.9

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

5. Applied rewrites 67.9%

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

Alternative 5: 29.5% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

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

   1. remove-double-neg N/A

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

   2. mul-1-neg N/A

      \[\leadsto {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{-1 \cdot \left(x + \frac{z}{y}\right)}\right)\right) \]

   3. distribute-lft-out N/A

      \[\leadsto {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)}\right)\right) \]

   4. distribute-rgt-neg-out N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)} \]

   5. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - {y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)} \]

   6. unsub-neg N/A

      \[\leadsto \color{blue}{0 + \left(\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right)} \]

   7. mul0-rgt N/A

      \[\leadsto \color{blue}{y \cdot 0} + \left(\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right) \]

   8. distribute-rgt-neg-out N/A

      \[\leadsto y \cdot 0 + \color{blue}{{y}^{2} \cdot \left(\mathsf{neg}\left(\left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right)} \]

   9. distribute-lft-out N/A

      \[\leadsto y \cdot 0 + {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{-1 \cdot \left(x + \frac{z}{y}\right)}\right)\right) \]

   10. mul-1-neg N/A

       \[\leadsto y \cdot 0 + {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\left(x + \frac{z}{y}\right)\right)\right)}\right)\right) \]

   11. remove-double-neg N/A

       \[\leadsto y \cdot 0 + {y}^{2} \cdot \color{blue}{\left(x + \frac{z}{y}\right)} \]

   12. unpow2 N/A

       \[\leadsto y \cdot 0 + \color{blue}{\left(y \cdot y\right)} \cdot \left(x + \frac{z}{y}\right) \]

   13. associate-*l* N/A

       \[\leadsto y \cdot 0 + \color{blue}{y \cdot \left(y \cdot \left(x + \frac{z}{y}\right)\right)} \]

   14. distribute-lft-in N/A

       \[\leadsto \color{blue}{y \cdot \left(0 + y \cdot \left(x + \frac{z}{y}\right)\right)} \]

   15. +-lft-identity N/A

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

   16. distribute-rgt-in N/A

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

   17. cancel-sign-sub N/A

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

   18. mul-1-neg N/A

       \[\leadsto y \cdot \left(x \cdot y - \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \cdot y\right) \]

5. Applied rewrites 59.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 28.7%

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

Reproduce

herbie shell --seed 2024318 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))