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

Percentage Accurate: 99.8% → 99.8%

Time: 7.1s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(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 = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(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 = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \mathsf{fma}\left(y, \sqrt{z}, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 (fma y (sqrt z) x)))

C

double code(double x, double y, double z) {
	return 0.5 * fma(y, sqrt(z), x);
}

Julia

function code(x, y, z)
	return Float64(0.5 * fma(y, sqrt(z), x))
end

Wolfram

code[x_, y_, z_] := N[(0.5 * N[(y * N[Sqrt[z], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+48} \lor \neg \left(x \leq 1.2 \cdot 10^{-8}\right):\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{{z}^{-0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.6e+48) (not (<= x 1.2e-8)))
   (* 0.5 x)
   (* 0.5 (/ y (pow z -0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e+48) || !(x <= 1.2e-8)) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * (y / pow(z, -0.5));
	}
	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 ((x <= (-4.6d+48)) .or. (.not. (x <= 1.2d-8))) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * (y / (z ** (-0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e+48) || !(x <= 1.2e-8)) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * (y / Math.pow(z, -0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.6e+48) or not (x <= 1.2e-8):
		tmp = 0.5 * x
	else:
		tmp = 0.5 * (y / math.pow(z, -0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.6e+48) || !(x <= 1.2e-8))
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * Float64(y / (z ^ -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.6e+48) || ~((x <= 1.2e-8)))
		tmp = 0.5 * x;
	else
		tmp = 0.5 * (y / (z ^ -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e+48], N[Not[LessEqual[x, 1.2e-8]], $MachinePrecision]], N[(0.5 * x), $MachinePrecision], N[(0.5 * N[(y / N[Power[z, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+51} \lor \neg \left(x \leq 6 \cdot 10^{-12}\right):\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z} \cdot \left(0.5 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+51) (not (<= x 6e-12))) (* 0.5 x) (* (sqrt z) (* 0.5 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+51) || !(x <= 6e-12)) {
		tmp = 0.5 * x;
	} else {
		tmp = sqrt(z) * (0.5 * y);
	}
	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 ((x <= (-7d+51)) .or. (.not. (x <= 6d-12))) then
        tmp = 0.5d0 * x
    else
        tmp = sqrt(z) * (0.5d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+51) || !(x <= 6e-12)) {
		tmp = 0.5 * x;
	} else {
		tmp = Math.sqrt(z) * (0.5 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+51) or not (x <= 6e-12):
		tmp = 0.5 * x
	else:
		tmp = math.sqrt(z) * (0.5 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+51) || !(x <= 6e-12))
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(sqrt(z) * Float64(0.5 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+51) || ~((x <= 6e-12)))
		tmp = 0.5 * x;
	else
		tmp = sqrt(z) * (0.5 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+51], N[Not[LessEqual[x, 6e-12]], $MachinePrecision]], N[(0.5 * x), $MachinePrecision], N[(N[Sqrt[z], $MachinePrecision] * N[(0.5 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return 0.5 * (x + (y * sqrt(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 = 0.5d0 * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return 0.5 * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(0.5 * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(0.5 * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 50.0% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 x))

C

double code(double x, double y, double z) {
	return 0.5 * 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 = 0.5d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * x;
}

Python

def code(x, y, z):
	return 0.5 * x

Julia

function code(x, y, z)
	return Float64(0.5 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * x;
end

Wolfram

code[x_, y_, z_] := N[(0.5 * x), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))