Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.2% → 99.2%

Time: 2.4s

Alternatives: 3

Speedup: 1.0×

• 24.3% 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

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

FPCore

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

C

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

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) - (t * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+78}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 10^{-80}:\\ \;\;\;\;\left(-t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* y x) -2e+78) (* y x) (if (<= (* y x) 1e-80) (* (- t) z) (* y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * x) <= -2e+78) {
		tmp = y * x;
	} else if ((y * x) <= 1e-80) {
		tmp = -t * z;
	} else {
		tmp = y * x;
	}
	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 ((y * x) <= (-2d+78)) then
        tmp = y * x
    else if ((y * x) <= 1d-80) then
        tmp = -t * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * x) <= -2e+78) {
		tmp = y * x;
	} else if ((y * x) <= 1e-80) {
		tmp = -t * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y * x) <= -2e+78:
		tmp = y * x
	elif (y * x) <= 1e-80:
		tmp = -t * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y * x) <= -2e+78)
		tmp = Float64(y * x);
	elseif (Float64(y * x) <= 1e-80)
		tmp = Float64(Float64(-t) * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y * x) <= -2e+78)
		tmp = y * x;
	elseif ((y * x) <= 1e-80)
		tmp = -t * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y * x), $MachinePrecision], -2e+78], N[(y * x), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e-80], N[((-t) * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000002e78 or 9.99999999999999961e-81 < (*.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.1

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

   5. Applied rewrites 84.1%

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

   if -2.00000000000000002e78 < (*.f64 x y) < 9.99999999999999961e-81

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 76.4

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

   5. Applied rewrites 76.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+78}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 10^{-80}:\\ \;\;\;\;\left(-t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.9% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 56.9

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

5. Applied rewrites 56.9%

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

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))