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

Percentage Accurate: 99.9% → 99.9%

Time: 6.6s

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 100.0%

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

   1. lift-*.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lower-fma.f64 100.0

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

   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 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 71.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \left(z + x \cdot y\right)\\ t_2 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y (+ z (* x y))))) (t_2 (* x (* y y))))
   (if (<= t_1 -1e+263) t_2 (if (<= t_1 INFINITY) (fma y z t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (y * (z + (x * y)));
	double t_2 = x * (y * y);
	double tmp;
	if (t_1 <= -1e+263) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(y * Float64(z + Float64(x * y))))
	t_2 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (t_1 <= -1e+263)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = fma(y, z, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+263], t$95$2, If[LessEqual[t$95$1, Infinity], N[(y * z + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) t) < -1.00000000000000002e263 or +inf.0 < (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) t)

   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 80.6

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

   5. Applied rewrites 80.6%

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 80.8

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

   7. Applied rewrites 80.8%

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

   if -1.00000000000000002e263 < (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) t) < +inf.0

   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 76.5

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

   5. Applied rewrites 76.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + y \cdot \left(z + x \cdot y\right) \leq -1 \cdot 10^{+263}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;t + y \cdot \left(z + x \cdot y\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ t_2 := y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1e+108) t_2 (if (<= t_1 6e+118) (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 <= -1e+108) {
		tmp = t_2;
	} else if (t_1 <= 6e+118) {
		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 <= -1e+108)
		tmp = t_2;
	elseif (t_1 <= 6e+118)
		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, -1e+108], t$95$2, If[LessEqual[t$95$1, 6e+118], N[(y * z + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -1e108 or 6e118 < (*.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 95.6%

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

   if -1e108 < (*.f64 (+.f64 (*.f64 x y) z) y) < 6e118

   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 92.1

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

   5. Applied rewrites 92.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z + x \cdot y\right) \leq -1 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \cdot \left(z + x \cdot y\right) \leq 6 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 14:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -1.8e+138) t_1 (if (<= y 14.0) (fma y z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.8e+138) {
		tmp = t_1;
	} else if (y <= 14.0) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -1.8e+138)
		tmp = t_1;
	elseif (y <= 14.0)
		tmp = fma(y, z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+138], t$95$1, If[LessEqual[y, 14.0], N[(y * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8000000000000001e138 or 14 < 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. 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 75.7

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

   5. Applied rewrites 75.7%

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

   if -1.8000000000000001e138 < y < 14

   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 88.1

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

   5. Applied rewrites 88.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 14:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% 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 68.2

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

5. Applied rewrites 68.2%

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

Alternative 6: 29.3% 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 30.8

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

5. Applied rewrites 30.8%

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

Reproduce

herbie shell --seed 2024214 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))