Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((y * 4.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((y * 4.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((y * 4.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((y * 4.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, y \cdot -4, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma z (* y -4.0) x))

C

double code(double x, double y, double z) {
	return fma(z, (y * -4.0), x);
}

Julia

function code(x, y, z)
	return fma(z, Float64(y * -4.0), x)
end

Wolfram

code[x_, y_, z_] := N[(z * N[(y * -4.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{x + \left(-\left(y \cdot 4\right) \cdot z\right)} \]

   2. distribute-rgt-neg-out 100.0%

      \[\leadsto x + \color{blue}{\left(y \cdot 4\right) \cdot \left(-z\right)} \]

   3. +-commutative 100.0%

      \[\leadsto \color{blue}{\left(y \cdot 4\right) \cdot \left(-z\right) + x} \]

   4. distribute-rgt-neg-out 100.0%

      \[\leadsto \color{blue}{\left(-\left(y \cdot 4\right) \cdot z\right)} + x \]

   5. distribute-lft-neg-in 100.0%

      \[\leadsto \color{blue}{\left(-y \cdot 4\right) \cdot z} + x \]

   6. *-commutative 100.0%

      \[\leadsto \color{blue}{z \cdot \left(-y \cdot 4\right)} + x \]

   7. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -y \cdot 4, x\right)} \]

   8. distribute-rgt-neg-in 100.0%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{y \cdot \left(-4\right)}, x\right) \]

   9. metadata-eval 100.0%

      \[\leadsto \mathsf{fma}\left(z, y \cdot \color{blue}{-4}, x\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, y \cdot -4, x\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(z, y \cdot -4, x\right) \]

Alternative 2: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+83} \lor \neg \left(y \leq -4.7 \cdot 10^{+51} \lor \neg \left(y \leq -0.0003\right) \land y \leq 4.1 \cdot 10^{-73}\right):\\ \;\;\;\;-4 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+83)
         (not (or (<= y -4.7e+51) (and (not (<= y -0.0003)) (<= y 4.1e-73)))))
   (* -4.0 (* z y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+83) || !((y <= -4.7e+51) || (!(y <= -0.0003) && (y <= 4.1e-73)))) {
		tmp = -4.0 * (z * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.2d+83)) .or. (.not. (y <= (-4.7d+51)) .or. (.not. (y <= (-0.0003d0))) .and. (y <= 4.1d-73))) then
        tmp = (-4.0d0) * (z * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+83) || !((y <= -4.7e+51) || (!(y <= -0.0003) && (y <= 4.1e-73)))) {
		tmp = -4.0 * (z * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+83) or not ((y <= -4.7e+51) or (not (y <= -0.0003) and (y <= 4.1e-73))):
		tmp = -4.0 * (z * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+83) || !((y <= -4.7e+51) || (!(y <= -0.0003) && (y <= 4.1e-73))))
		tmp = Float64(-4.0 * Float64(z * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e+83) || ~(((y <= -4.7e+51) || (~((y <= -0.0003)) && (y <= 4.1e-73)))))
		tmp = -4.0 * (z * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+83], N[Not[Or[LessEqual[y, -4.7e+51], And[N[Not[LessEqual[y, -0.0003]], $MachinePrecision], LessEqual[y, 4.1e-73]]]], $MachinePrecision]], N[(-4.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000005e83 or -4.7000000000000002e51 < y < -2.99999999999999974e-4 or 4.10000000000000016e-73 < y

   1. Initial program 99.9%

      \[x - \left(y \cdot 4\right) \cdot z \]

   2. Taylor expanded in x around 0 71.4%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot z\right)} \]

   if -4.20000000000000005e83 < y < -4.7000000000000002e51 or -2.99999999999999974e-4 < y < 4.10000000000000016e-73

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]

   2. Taylor expanded in x around inf 74.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+83} \lor \neg \left(y \leq -4.7 \cdot 10^{+51} \lor \neg \left(y \leq -0.0003\right) \land y \leq 4.1 \cdot 10^{-73}\right):\\ \;\;\;\;-4 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - z \cdot \left(y \cdot 4\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* z (* y 4.0))))

C

double code(double x, double y, double z) {
	return x - (z * (y * 4.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - (z * (y * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x - (z * (y * 4.0));
}

Python

def code(x, y, z):
	return x - (z * (y * 4.0))

Julia

function code(x, y, z)
	return Float64(x - Float64(z * Float64(y * 4.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - (z * (y * 4.0));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]

2. Final simplification 100.0%

   \[\leadsto x - z \cdot \left(y \cdot 4\right) \]

Alternative 4: 50.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]

2. Taylor expanded in x around inf 49.1%

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

3. Final simplification 49.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023285 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))