Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.2% → 99.2%

Time: 3.0s

Alternatives: 3

Speedup: 1.0×

• 23.7% 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: 99.2% 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]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 71.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+267} \lor \neg \left(x \cdot y \leq -3.7 \cdot 10^{+224} \lor \neg \left(x \cdot y \leq -1.65 \cdot 10^{+101}\right) \land \left(x \cdot y \leq -4.5 \cdot 10^{-5} \lor \neg \left(x \cdot y \leq -6.8 \cdot 10^{-36}\right) \land \left(x \cdot y \leq 7.6 \cdot 10^{-145} \lor \neg \left(x \cdot y \leq 4.6 \cdot 10^{-55}\right) \land x \cdot y \leq 2.25 \cdot 10^{+70}\right)\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x y) -2e+267)
         (not
          (or (<= (* x y) -3.7e+224)
              (and (not (<= (* x y) -1.65e+101))
                   (or (<= (* x y) -4.5e-5)
                       (and (not (<= (* x y) -6.8e-36))
                            (or (<= (* x y) 7.6e-145)
                                (and (not (<= (* x y) 4.6e-55))
                                     (<= (* x y) 2.25e+70)))))))))
   (* x y)
   (* z (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * y) <= -2e+267) || !(((x * y) <= -3.7e+224) || (!((x * y) <= -1.65e+101) && (((x * y) <= -4.5e-5) || (!((x * y) <= -6.8e-36) && (((x * y) <= 7.6e-145) || (!((x * y) <= 4.6e-55) && ((x * y) <= 2.25e+70)))))))) {
		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) <= (-2d+267)) .or. (.not. ((x * y) <= (-3.7d+224)) .or. (.not. ((x * y) <= (-1.65d+101))) .and. ((x * y) <= (-4.5d-5)) .or. (.not. ((x * y) <= (-6.8d-36))) .and. ((x * y) <= 7.6d-145) .or. (.not. ((x * y) <= 4.6d-55)) .and. ((x * y) <= 2.25d+70))) 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) <= -2e+267) || !(((x * y) <= -3.7e+224) || (!((x * y) <= -1.65e+101) && (((x * y) <= -4.5e-5) || (!((x * y) <= -6.8e-36) && (((x * y) <= 7.6e-145) || (!((x * y) <= 4.6e-55) && ((x * y) <= 2.25e+70)))))))) {
		tmp = x * y;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * y) <= -2e+267) or not (((x * y) <= -3.7e+224) or (not ((x * y) <= -1.65e+101) and (((x * y) <= -4.5e-5) or (not ((x * y) <= -6.8e-36) and (((x * y) <= 7.6e-145) or (not ((x * y) <= 4.6e-55) and ((x * y) <= 2.25e+70))))))):
		tmp = x * y
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+267) || !((Float64(x * y) <= -3.7e+224) || (!(Float64(x * y) <= -1.65e+101) && ((Float64(x * y) <= -4.5e-5) || (!(Float64(x * y) <= -6.8e-36) && ((Float64(x * y) <= 7.6e-145) || (!(Float64(x * y) <= 4.6e-55) && (Float64(x * y) <= 2.25e+70))))))))
		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) <= -2e+267) || ~((((x * y) <= -3.7e+224) || (~(((x * y) <= -1.65e+101)) && (((x * y) <= -4.5e-5) || (~(((x * y) <= -6.8e-36)) && (((x * y) <= 7.6e-145) || (~(((x * y) <= 4.6e-55)) && ((x * y) <= 2.25e+70)))))))))
		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], -2e+267], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], -3.7e+224], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -1.65e+101]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -4.5e-5], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -6.8e-36]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 7.6e-145], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.6e-55]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 2.25e+70]]]]]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e267 or -3.70000000000000003e224 < (*.f64 x y) < -1.65000000000000006e101 or -4.50000000000000028e-5 < (*.f64 x y) < -6.8000000000000005e-36 or 7.6000000000000004e-145 < (*.f64 x y) < 4.60000000000000023e-55 or 2.25e70 < (*.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.7%

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

   if -1.9999999999999999e267 < (*.f64 x y) < -3.70000000000000003e224 or -1.65000000000000006e101 < (*.f64 x y) < -4.50000000000000028e-5 or -6.8000000000000005e-36 < (*.f64 x y) < 7.6000000000000004e-145 or 4.60000000000000023e-55 < (*.f64 x y) < 2.25e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.5%

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

      1. associate-*r* 79.5%

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

      2. neg-mul-1 79.5%

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

      3. *-commutative 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+267} \lor \neg \left(x \cdot y \leq -3.7 \cdot 10^{+224} \lor \neg \left(x \cdot y \leq -1.65 \cdot 10^{+101}\right) \land \left(x \cdot y \leq -4.5 \cdot 10^{-5} \lor \neg \left(x \cdot y \leq -6.8 \cdot 10^{-36}\right) \land \left(x \cdot y \leq 7.6 \cdot 10^{-145} \lor \neg \left(x \cdot y \leq 4.6 \cdot 10^{-55}\right) \land x \cdot y \leq 2.25 \cdot 10^{+70}\right)\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% 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 100.0%

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

3. Taylor expanded in x around inf 47.8%

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

4. Final simplification 47.8%

   \[\leadsto x \cdot y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))