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

Percentage Accurate: 99.9% → 99.9%

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: 99.9% 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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(y * N[(z * -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. associate-*l* 100.0%

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

   5. distribute-rgt-neg-in 100.0%

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

   6. *-commutative 100.0%

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

   7. fma-def 100.0%

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

   8. distribute-rgt-neg-in 100.0%

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

   9. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 69.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+123} \lor \neg \left(y \leq -9.5 \cdot 10^{+105} \lor \neg \left(y \leq -2 \cdot 10^{+77}\right) \land \left(y \leq -1.1 \cdot 10^{+43} \lor \neg \left(y \leq -1.75 \cdot 10^{-24}\right) \land y \leq 2.4 \cdot 10^{-91}\right)\right):\\ \;\;\;\;z \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.6e+123)
         (not
          (or (<= y -9.5e+105)
              (and (not (<= y -2e+77))
                   (or (<= y -1.1e+43)
                       (and (not (<= y -1.75e-24)) (<= y 2.4e-91)))))))
   (* z (* y -4.0))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.6e+123) || !((y <= -9.5e+105) || (!(y <= -2e+77) && ((y <= -1.1e+43) || (!(y <= -1.75e-24) && (y <= 2.4e-91)))))) {
		tmp = z * (y * -4.0);
	} 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 <= (-8.6d+123)) .or. (.not. (y <= (-9.5d+105)) .or. (.not. (y <= (-2d+77))) .and. (y <= (-1.1d+43)) .or. (.not. (y <= (-1.75d-24))) .and. (y <= 2.4d-91))) then
        tmp = z * (y * (-4.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.6e+123) || !((y <= -9.5e+105) || (!(y <= -2e+77) && ((y <= -1.1e+43) || (!(y <= -1.75e-24) && (y <= 2.4e-91)))))) {
		tmp = z * (y * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.6e+123) or not ((y <= -9.5e+105) or (not (y <= -2e+77) and ((y <= -1.1e+43) or (not (y <= -1.75e-24) and (y <= 2.4e-91))))):
		tmp = z * (y * -4.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.6e+123) || !((y <= -9.5e+105) || (!(y <= -2e+77) && ((y <= -1.1e+43) || (!(y <= -1.75e-24) && (y <= 2.4e-91))))))
		tmp = Float64(z * Float64(y * -4.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.6e+123) || ~(((y <= -9.5e+105) || (~((y <= -2e+77)) && ((y <= -1.1e+43) || (~((y <= -1.75e-24)) && (y <= 2.4e-91)))))))
		tmp = z * (y * -4.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.6e+123], N[Not[Or[LessEqual[y, -9.5e+105], And[N[Not[LessEqual[y, -2e+77]], $MachinePrecision], Or[LessEqual[y, -1.1e+43], And[N[Not[LessEqual[y, -1.75e-24]], $MachinePrecision], LessEqual[y, 2.4e-91]]]]]], $MachinePrecision]], N[(z * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.59999999999999972e123 or -9.4999999999999995e105 < y < -1.99999999999999997e77 or -1.1e43 < y < -1.7499999999999998e-24 or 2.40000000000000011e-91 < y

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   if -8.59999999999999972e123 < y < -9.4999999999999995e105 or -1.99999999999999997e77 < y < -1.1e43 or -1.7499999999999998e-24 < y < 2.40000000000000011e-91

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+123} \lor \neg \left(y \leq -9.5 \cdot 10^{+105} \lor \neg \left(y \leq -2 \cdot 10^{+77}\right) \land \left(y \leq -1.1 \cdot 10^{+43} \lor \neg \left(y \leq -1.75 \cdot 10^{-24}\right) \land y \leq 2.4 \cdot 10^{-91}\right)\right):\\ \;\;\;\;z \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 4: 51.2% 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. Add Preprocessing

3. Taylor expanded in x around inf 51.1%

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

4. Final simplification 51.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))