Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.2% → 99.6%

Time: 2.1s

Alternatives: 4

Speedup: 1.0×

• 23.6% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-lft-neg-in 100.0%

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

   4. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+61} \lor \neg \left(z \leq -6.2 \cdot 10^{+54} \lor \neg \left(z \leq -2.1 \cdot 10^{-28}\right) \land z \leq 2.25 \cdot 10^{-122}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e+61)
         (not
          (or (<= z -6.2e+54) (and (not (<= z -2.1e-28)) (<= z 2.25e-122)))))
   (* z (- t))
   (* x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+61) || !((z <= -6.2e+54) || (!(z <= -2.1e-28) && (z <= 2.25e-122)))) {
		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 ((z <= (-1.65d+61)) .or. (.not. (z <= (-6.2d+54)) .or. (.not. (z <= (-2.1d-28))) .and. (z <= 2.25d-122))) 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 ((z <= -1.65e+61) || !((z <= -6.2e+54) || (!(z <= -2.1e-28) && (z <= 2.25e-122)))) {
		tmp = z * -t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e+61) or not ((z <= -6.2e+54) or (not (z <= -2.1e-28) and (z <= 2.25e-122))):
		tmp = z * -t
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e+61) || !((z <= -6.2e+54) || (!(z <= -2.1e-28) && (z <= 2.25e-122))))
		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 ((z <= -1.65e+61) || ~(((z <= -6.2e+54) || (~((z <= -2.1e-28)) && (z <= 2.25e-122)))))
		tmp = z * -t;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e+61], N[Not[Or[LessEqual[z, -6.2e+54], And[N[Not[LessEqual[z, -2.1e-28]], $MachinePrecision], LessEqual[z, 2.25e-122]]]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e61 or -6.1999999999999999e54 < z < -2.10000000000000006e-28 or 2.2499999999999999e-122 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.6%

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

      1. associate-*r* 69.6%

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

      2. neg-mul-1 69.6%

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

      3. *-commutative 69.6%

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

   4. Simplified 69.6%

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

   if -1.6499999999999999e61 < z < -6.1999999999999999e54 or -2.10000000000000006e-28 < z < 2.2499999999999999e-122

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+61} \lor \neg \left(z \leq -6.2 \cdot 10^{+54} \lor \neg \left(z \leq -2.1 \cdot 10^{-28}\right) \land z \leq 2.25 \cdot 10^{-122}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 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. Final simplification 100.0%

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

Alternative 4: 52.9% 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. Taylor expanded in x around inf 52.8%

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

3. Final simplification 52.8%

   \[\leadsto x \cdot y \]

Reproduce

herbie shell --seed 2023214 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))