Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.1% → 99.6%

Time: 8.8s

Alternatives: 4

Speedup: 1.0×

• 23.8% 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: 99.1% 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

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, 0 - z \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma y x (- 0.0 (* z t))))

C

double code(double x, double y, double z, double t) {
	return fma(y, x, (0.0 - (z * t)));
}

Julia

function code(x, y, z, t)
	return fma(y, x, Float64(0.0 - Float64(z * t)))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * x + N[(0.0 - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. sub-neg N/A

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

   2. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{x}, \left(\mathsf{neg}\left(z \cdot t\right)\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \left(0 - z \cdot t\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(0, \left(z \cdot t\right)\right)\right) \]

   6. *-lowering-*.f64 99.6%

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, t\right)\right)\right) \]

4. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 0 - z \cdot t\right)} \]
5. Add Preprocessing

Alternative 2: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -3.6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;0 - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* y x) -3.6e-83)
   (* y x)
   (if (<= (* y x) 7.2e-42) (- 0.0 (* z t)) (* y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * x) <= -3.6e-83) {
		tmp = y * x;
	} else if ((y * x) <= 7.2e-42) {
		tmp = 0.0 - (z * t);
	} 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) <= (-3.6d-83)) then
        tmp = y * x
    else if ((y * x) <= 7.2d-42) then
        tmp = 0.0d0 - (z * t)
    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) <= -3.6e-83) {
		tmp = y * x;
	} else if ((y * x) <= 7.2e-42) {
		tmp = 0.0 - (z * t);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y * x) <= -3.6e-83:
		tmp = y * x
	elif (y * x) <= 7.2e-42:
		tmp = 0.0 - (z * t)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y * x) <= -3.6e-83)
		tmp = Float64(y * x);
	elseif (Float64(y * x) <= 7.2e-42)
		tmp = Float64(0.0 - Float64(z * t));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y * x) <= -3.6e-83)
		tmp = y * x;
	elseif ((y * x) <= 7.2e-42)
		tmp = 0.0 - (z * t);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y * x), $MachinePrecision], -3.6e-83], N[(y * x), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 7.2e-42], N[(0.0 - N[(z * t), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.60000000000000012e-83 or 7.2000000000000004e-42 < (*.f64 x y)

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 79.4%

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

   if -3.60000000000000012e-83 < (*.f64 x y) < 7.2000000000000004e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{t \cdot z} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 87.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 87.4%

      \[\leadsto \color{blue}{0 - t \cdot z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(z \cdot t\right)\right) \]

      4. *-lowering-*.f64 87.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, t\right)\right) \]

   7. Applied egg-rr 87.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -3.6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;0 - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Final simplification 99.2%

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

Alternative 4: 51.2% 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 99.2%

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

3. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 54.1%

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

5. Simplified 54.1%

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

6. Final simplification 54.1%

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

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))