Linear.V2:$cdot from linear-1.19.1.3, A

Percentage Accurate: 99.2% → 99.6%

Time: 1.6s

Alternatives: 4

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot y + z \cdot t \]
2. Step-by-step derivation

   1. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+77} \lor \neg \left(t \leq 1.15 \cdot 10^{+39}\right) \land \left(t \leq 1.3 \cdot 10^{+135} \lor \neg \left(t \leq 8.2 \cdot 10^{+144}\right)\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.6e+77)
         (and (not (<= t 1.15e+39))
              (or (<= t 1.3e+135) (not (<= t 8.2e+144)))))
   (* z t)
   (* x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e+77) || (!(t <= 1.15e+39) && ((t <= 1.3e+135) || !(t <= 8.2e+144)))) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	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) :: tmp
    if ((t <= (-4.6d+77)) .or. (.not. (t <= 1.15d+39)) .and. (t <= 1.3d+135) .or. (.not. (t <= 8.2d+144))) then
        tmp = z * t
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e+77) || (!(t <= 1.15e+39) && ((t <= 1.3e+135) || !(t <= 8.2e+144)))) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.6e+77) or (not (t <= 1.15e+39) and ((t <= 1.3e+135) or not (t <= 8.2e+144))):
		tmp = z * t
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.6e+77) || (!(t <= 1.15e+39) && ((t <= 1.3e+135) || !(t <= 8.2e+144))))
		tmp = Float64(z * t);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.6e+77) || (~((t <= 1.15e+39)) && ((t <= 1.3e+135) || ~((t <= 8.2e+144)))))
		tmp = z * t;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.6e+77], And[N[Not[LessEqual[t, 1.15e+39]], $MachinePrecision], Or[LessEqual[t, 1.3e+135], N[Not[LessEqual[t, 8.2e+144]], $MachinePrecision]]]], N[(z * t), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999999e77 or 1.15000000000000006e39 < t < 1.3e135 or 8.20000000000000002e144 < t

   1. Initial program 100.0%

      \[x \cdot y + z \cdot t \]

   2. Taylor expanded in x around 0 73.6%

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

   if -4.5999999999999999e77 < t < 1.15000000000000006e39 or 1.3e135 < t < 8.20000000000000002e144

   1. Initial program 100.0%

      \[x \cdot y + z \cdot t \]

   2. Taylor expanded in x around inf 68.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+77} \lor \neg \left(t \leq 1.15 \cdot 10^{+39}\right) \land \left(t \leq 1.3 \cdot 10^{+135} \lor \neg \left(t \leq 8.2 \cdot 10^{+144}\right)\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot y + z \cdot t \]

2. Final simplification 100.0%

   \[\leadsto z \cdot t + x \cdot y \]

Alternative 4: 53.0% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot y + z \cdot t \]

2. Taylor expanded in x around 0 51.8%

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

3. Final simplification 51.8%

   \[\leadsto z \cdot t \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))