Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.3% → 99.3%

Time: 3.8s

Alternatives: 3

Speedup: 1.0×

• 24.2% 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: 99.3% 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: 99.3% 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]

Derivation

1. Initial program 99.6%

   \[x \cdot y - z \cdot t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq -5.5 \cdot 10^{-192}\right) \land \left(x \cdot y \leq -1.5 \cdot 10^{-282} \lor \neg \left(x \cdot y \leq 1.45 \cdot 10^{-5}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x y) -1.95e-16)
         (and (not (<= (* x y) -5.5e-192))
              (or (<= (* x y) -1.5e-282) (not (<= (* x y) 1.45e-5)))))
   (* x y)
   (* z (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * y) <= -1.95e-16) || (!((x * y) <= -5.5e-192) && (((x * y) <= -1.5e-282) || !((x * y) <= 1.45e-5)))) {
		tmp = x * y;
	} else {
		tmp = z * -t;
	}
	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 (((x * y) <= (-1.95d-16)) .or. (.not. ((x * y) <= (-5.5d-192))) .and. ((x * y) <= (-1.5d-282)) .or. (.not. ((x * y) <= 1.45d-5))) then
        tmp = x * y
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * y) <= -1.95e-16) || (!((x * y) <= -5.5e-192) && (((x * y) <= -1.5e-282) || !((x * y) <= 1.45e-5)))) {
		tmp = x * y;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * y) <= -1.95e-16) or (not ((x * y) <= -5.5e-192) and (((x * y) <= -1.5e-282) or not ((x * y) <= 1.45e-5))):
		tmp = x * y
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * y) <= -1.95e-16) || (!(Float64(x * y) <= -5.5e-192) && ((Float64(x * y) <= -1.5e-282) || !(Float64(x * y) <= 1.45e-5))))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * y) <= -1.95e-16) || (~(((x * y) <= -5.5e-192)) && (((x * y) <= -1.5e-282) || ~(((x * y) <= 1.45e-5)))))
		tmp = x * y;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.95e-16], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -5.5e-192]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -1.5e-282], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.45e-5]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.94999999999999989e-16 or -5.49999999999999995e-192 < (*.f64 x y) < -1.5e-282 or 1.45e-5 < (*.f64 x y)

   1. Initial program 99.3%

      \[x \cdot y - z \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.7%

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

   if -1.94999999999999989e-16 < (*.f64 x y) < -5.49999999999999995e-192 or -1.5e-282 < (*.f64 x y) < 1.45e-5

   1. Initial program 100.0%

      \[x \cdot y - z \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 82.1%

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

      2. neg-mul-1 82.1%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot z \]

      3. *-commutative 82.1%

         \[\leadsto \color{blue}{z \cdot \left(-t\right)} \]

   5. Simplified 82.1%

      \[\leadsto \color{blue}{z \cdot \left(-t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq -5.5 \cdot 10^{-192}\right) \land \left(x \cdot y \leq -1.5 \cdot 10^{-282} \lor \neg \left(x \cdot y \leq 1.45 \cdot 10^{-5}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x \cdot y - z \cdot t \]
2. Add Preprocessing

3. Taylor expanded in x around inf 51.2%

   \[\leadsto \color{blue}{x \cdot y} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))