Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.3% → 99.6%

Time: 1.7s

Alternatives: 4

Speedup: 1.0×

• 22.8% 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: 99.6% accurate, 0.1× speedup

Math

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

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 * Float64(-t)))
end

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. fma-neg 100.0%

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

   2. distribute-rgt-neg-in 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-100} \lor \neg \left(t \leq 1.15 \cdot 10^{-17} \lor \neg \left(t \leq 3.3 \cdot 10^{+18}\right) \land t \leq 2.9 \cdot 10^{+53}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.4e-100)
         (not (or (<= t 1.15e-17) (and (not (<= t 3.3e+18)) (<= t 2.9e+53)))))
   (* z (- t))
   (* x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e-100) || !((t <= 1.15e-17) || (!(t <= 3.3e+18) && (t <= 2.9e+53)))) {
		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 <= (-4.4d-100)) .or. (.not. (t <= 1.15d-17) .or. (.not. (t <= 3.3d+18)) .and. (t <= 2.9d+53))) 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 <= -4.4e-100) || !((t <= 1.15e-17) || (!(t <= 3.3e+18) && (t <= 2.9e+53)))) {
		tmp = z * -t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.4e-100) or not ((t <= 1.15e-17) or (not (t <= 3.3e+18) and (t <= 2.9e+53))):
		tmp = z * -t
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.4e-100) || !((t <= 1.15e-17) || (!(t <= 3.3e+18) && (t <= 2.9e+53))))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.4e-100) || ~(((t <= 1.15e-17) || (~((t <= 3.3e+18)) && (t <= 2.9e+53)))))
		tmp = z * -t;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.4e-100], N[Not[Or[LessEqual[t, 1.15e-17], And[N[Not[LessEqual[t, 3.3e+18]], $MachinePrecision], LessEqual[t, 2.9e+53]]]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.39999999999999978e-100 or 1.15000000000000004e-17 < t < 3.3e18 or 2.9000000000000002e53 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 73.8%

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

      1. associate-*r* 73.8%

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

      2. neg-mul-1 73.8%

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

      3. *-commutative 73.8%

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

   4. Simplified 73.8%

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

   if -4.39999999999999978e-100 < t < 1.15000000000000004e-17 or 3.3e18 < t < 2.9000000000000002e53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-100} \lor \neg \left(t \leq 1.15 \cdot 10^{-17} \lor \neg \left(t \leq 3.3 \cdot 10^{+18}\right) \land t \leq 2.9 \cdot 10^{+53}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 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. Final simplification 99.6%

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

Alternative 4: 52.8% 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 99.6%

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

2. Taylor expanded in x around inf 51.5%

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

3. Final simplification 51.5%

   \[\leadsto x \cdot y \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))