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

Percentage Accurate: 99.9% → 99.9%

Time: 9.1s

Alternatives: 7

Speedup: 1.0×

• 28.8% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 51.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y + z\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ (* x y) z))))
   (if (<= t_1 -5e+53) (* y z) (if (<= t_1 2e-83) t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * ((x * y) + z);
	double tmp;
	if (t_1 <= -5e+53) {
		tmp = y * z;
	} else if (t_1 <= 2e-83) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * y) + z)
    if (t_1 <= (-5d+53)) then
        tmp = y * z
    else if (t_1 <= 2d-83) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * ((x * y) + z);
	double tmp;
	if (t_1 <= -5e+53) {
		tmp = y * z;
	} else if (t_1 <= 2e-83) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * ((x * y) + z)
	tmp = 0
	if t_1 <= -5e+53:
		tmp = y * z
	elif t_1 <= 2e-83:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(x * y) + z))
	tmp = 0.0
	if (t_1 <= -5e+53)
		tmp = Float64(y * z);
	elseif (t_1 <= 2e-83)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * ((x * y) + z);
	tmp = 0.0;
	if (t_1 <= -5e+53)
		tmp = y * z;
	elseif (t_1 <= 2e-83)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+53], N[(y * z), $MachinePrecision], If[LessEqual[t$95$1, 2e-83], t, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -5.0000000000000004e53 or 2.0000000000000001e-83 < (*.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 z around inf

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

      1. *-lowering-*.f64 40.5

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

   5. Simplified 40.5%

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

   if -5.0000000000000004e53 < (*.f64 (+.f64 (*.f64 x y) z) y) < 2.0000000000000001e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 80.3%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot y + z\right) \leq -5 \cdot 10^{+53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \cdot \left(x \cdot y + z\right) \leq 2 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -45000000000000:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -45000000000000.0)
   (* y (fma y x z))
   (if (<= y 4.5e-72) (fma y z t) (* y (+ (* x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -45000000000000.0) {
		tmp = y * fma(y, x, z);
	} else if (y <= 4.5e-72) {
		tmp = fma(y, z, t);
	} else {
		tmp = y * ((x * y) + z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -45000000000000.0)
		tmp = Float64(y * fma(y, x, z));
	elseif (y <= 4.5e-72)
		tmp = fma(y, z, t);
	else
		tmp = Float64(y * Float64(Float64(x * y) + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -45000000000000.0], N[(y * N[(y * x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-72], N[(y * z + t), $MachinePrecision], N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e13

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 97.2%

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

   if -4.5e13 < y < 4.5e-72

   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. accelerator-lowering-fma.f64 95.9

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

   5. Simplified 95.9%

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

   if 4.5e-72 < 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. Simplified 84.8%

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

      1. *-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 84.8

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

   7. Applied egg-rr 84.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -45000000000000:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(y, x, z\right)\\ \mathbf{if}\;y \leq -15500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (fma y x z))))
   (if (<= y -15500000000.0) t_1 (if (<= y 4.5e-72) (fma y z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * fma(y, x, z);
	double tmp;
	if (y <= -15500000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e-72) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * fma(y, x, z))
	tmp = 0.0
	if (y <= -15500000000.0)
		tmp = t_1;
	elseif (y <= 4.5e-72)
		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[(y * x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -15500000000.0], t$95$1, If[LessEqual[y, 4.5e-72], N[(y * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e10 or 4.5e-72 < 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. Simplified 90.6%

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

   if -1.55e10 < y < 4.5e-72

   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. accelerator-lowering-fma.f64 95.9

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

   5. Simplified 95.9%

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

Alternative 5: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -2.7e+21) t_1 (if (<= y 8.8e+173) (fma y z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -2.7e+21) {
		tmp = t_1;
	} else if (y <= 8.8e+173) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -2.7e+21)
		tmp = t_1;
	elseif (y <= 8.8e+173)
		tmp = fma(y, z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+21], t$95$1, If[LessEqual[y, 8.8e+173], N[(y * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e21 or 8.7999999999999999e173 < y

   1. Initial program 99.9%

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 87.0

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

   4. Applied egg-rr 87.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 77.6

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

   7. Simplified 77.6%

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

   if -2.7e21 < y < 8.7999999999999999e173

   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. accelerator-lowering-fma.f64 85.0

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

   5. Simplified 85.0%

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

Alternative 6: 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 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. accelerator-lowering-fma.f64 65.9

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

5. Simplified 65.9%

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

Alternative 7: 38.7% accurate, 17.0× 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. Add Preprocessing

3. Taylor expanded in y around 0

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

5. Simplified 35.6%

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

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))