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

Percentage Accurate: 99.9% → 99.9%

Time: 7.5s

Alternatives: 6

Speedup: 1.3×

• 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, 1.3× 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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lower-fma.f64 99.9

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

   4. lift-+.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lower-fma.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ t_2 := y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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+60) t_2 (if (<= t_1 5e+98) (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+60) {
		tmp = t_2;
	} else if (t_1 <= 5e+98) {
		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+60)
		tmp = t_2;
	elseif (t_1 <= 5e+98)
		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+60], t$95$2, If[LessEqual[t$95$1, 5e+98], N[(y * z + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -1.9999999999999999e60 or 4.9999999999999998e98 < (*.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 94.8%

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

   if -1.9999999999999999e60 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.9999999999999998e98

   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. lower-fma.f64 91.5

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

   5. Applied rewrites 91.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z + x \cdot y\right) \leq -2 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \cdot \left(z + x \cdot y\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+236}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= t_1 -1e+236)
     (* y (* x y))
     (if (<= t_1 5e+261) (fma y z t) (* x (* y y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (t_1 <= -1e+236) {
		tmp = y * (x * y);
	} else if (t_1 <= 5e+261) {
		tmp = fma(y, z, t);
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (t_1 <= -1e+236)
		tmp = Float64(y * Float64(x * y));
	elseif (t_1 <= 5e+261)
		tmp = fma(y, z, t);
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+236], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+261], N[(y * z + t), $MachinePrecision], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -1.00000000000000005e236

   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. 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 90.4

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

   5. Applied rewrites 90.4%

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

   if -1.00000000000000005e236 < (*.f64 (+.f64 (*.f64 x y) z) y) < 5.0000000000000001e261

   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. lower-fma.f64 81.8

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

   5. Applied rewrites 81.8%

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

   if 5.0000000000000001e261 < (*.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 74.9

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

   5. Applied rewrites 74.9%

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

   7. Applied rewrites 79.7%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z + x \cdot y\right) \leq -1 \cdot 10^{+236}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot \left(z + x \cdot y\right) \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ t_2 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))) (t_2 (* y (* x y))))
   (if (<= t_1 -1e+236) t_2 (if (<= t_1 5e+261) (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 <= -1e+236) {
		tmp = t_2;
	} else if (t_1 <= 5e+261) {
		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 <= -1e+236)
		tmp = t_2;
	elseif (t_1 <= 5e+261)
		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, -1e+236], t$95$2, If[LessEqual[t$95$1, 5e+261], N[(y * z + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -1.00000000000000005e236 or 5.0000000000000001e261 < (*.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 84.1

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

   5. Applied rewrites 84.1%

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

   if -1.00000000000000005e236 < (*.f64 (+.f64 (*.f64 x y) z) y) < 5.0000000000000001e261

   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. lower-fma.f64 81.8

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

   5. Applied rewrites 81.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z + x \cdot y\right) \leq -1 \cdot 10^{+236}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot \left(z + x \cdot y\right) \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.4% 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 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. lower-fma.f64 61.1

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

5. Applied rewrites 61.1%

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

Alternative 6: 29.7% 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 99.9%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 26.6

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

5. Applied rewrites 26.6%

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

Reproduce

herbie shell --seed 2024221 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))