2isqrt (example 3.6)

Percentage Accurate: 68.9% → 99.4%

Time: 10.9s

Alternatives: 10

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

C

double code(double x) {
	return (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / sqrt(x)) - (1.0d0 / sqrt((x + 1.0d0)))
end function

Java

public static double code(double x) {
	return (1.0 / Math.sqrt(x)) - (1.0 / Math.sqrt((x + 1.0)));
}

Python

def code(x):
	return (1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))

Julia

function code(x)
	return Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0))))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
end

Wolfram

code[x_] := N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

C

double code(double x) {
	return (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / sqrt(x)) - (1.0d0 / sqrt((x + 1.0d0)))
end function

Java

public static double code(double x) {
	return (1.0 / Math.sqrt(x)) - (1.0 / Math.sqrt((x + 1.0)));
}

Python

def code(x):
	return (1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))

Julia

function code(x)
	return Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0))))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
end

Wolfram

code[x_] := N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1}{x}}{\left(1 + x\right) \cdot \left({x}^{-0.5} + {\left(1 + x\right)}^{-0.5}\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (/ 1.0 x) (* (+ 1.0 x) (+ (pow x -0.5) (pow (+ 1.0 x) -0.5)))))

C

double code(double x) {
	return (1.0 / x) / ((1.0 + x) * (pow(x, -0.5) + pow((1.0 + x), -0.5)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / x) / ((1.0d0 + x) * ((x ** (-0.5d0)) + ((1.0d0 + x) ** (-0.5d0))))
end function

Java

public static double code(double x) {
	return (1.0 / x) / ((1.0 + x) * (Math.pow(x, -0.5) + Math.pow((1.0 + x), -0.5)));
}

Python

def code(x):
	return (1.0 / x) / ((1.0 + x) * (math.pow(x, -0.5) + math.pow((1.0 + x), -0.5)))

Julia

function code(x)
	return Float64(Float64(1.0 / x) / Float64(Float64(1.0 + x) * Float64((x ^ -0.5) + (Float64(1.0 + x) ^ -0.5))))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / x) / ((1.0 + x) * ((x ^ -0.5) + ((1.0 + x) ^ -0.5)));
end

Wolfram

code[x_] := N[(N[(1.0 / x), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * N[(N[Power[x, -0.5], $MachinePrecision] + N[Power[N[(1.0 + x), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 2: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.7:\\ \;\;\;\;{x}^{-0.5} + \frac{-1}{1 + x \cdot 0.5}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;0.5 \cdot \sqrt{\frac{1}{{x}^{3}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{x}^{1.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.7)
   (+ (pow x -0.5) (/ -1.0 (+ 1.0 (* x 0.5))))
   (if (<= x 5.6e+102)
     (* 0.5 (sqrt (/ 1.0 (pow x 3.0))))
     (/ 1.0 (pow x 1.5)))))

C

double code(double x) {
	double tmp;
	if (x <= 1.7) {
		tmp = pow(x, -0.5) + (-1.0 / (1.0 + (x * 0.5)));
	} else if (x <= 5.6e+102) {
		tmp = 0.5 * sqrt((1.0 / pow(x, 3.0)));
	} else {
		tmp = 1.0 / pow(x, 1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.7d0) then
        tmp = (x ** (-0.5d0)) + ((-1.0d0) / (1.0d0 + (x * 0.5d0)))
    else if (x <= 5.6d+102) then
        tmp = 0.5d0 * sqrt((1.0d0 / (x ** 3.0d0)))
    else
        tmp = 1.0d0 / (x ** 1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.7) {
		tmp = Math.pow(x, -0.5) + (-1.0 / (1.0 + (x * 0.5)));
	} else if (x <= 5.6e+102) {
		tmp = 0.5 * Math.sqrt((1.0 / Math.pow(x, 3.0)));
	} else {
		tmp = 1.0 / Math.pow(x, 1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.7:
		tmp = math.pow(x, -0.5) + (-1.0 / (1.0 + (x * 0.5)))
	elif x <= 5.6e+102:
		tmp = 0.5 * math.sqrt((1.0 / math.pow(x, 3.0)))
	else:
		tmp = 1.0 / math.pow(x, 1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.7)
		tmp = Float64((x ^ -0.5) + Float64(-1.0 / Float64(1.0 + Float64(x * 0.5))));
	elseif (x <= 5.6e+102)
		tmp = Float64(0.5 * sqrt(Float64(1.0 / (x ^ 3.0))));
	else
		tmp = Float64(1.0 / (x ^ 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.7)
		tmp = (x ^ -0.5) + (-1.0 / (1.0 + (x * 0.5)));
	elseif (x <= 5.6e+102)
		tmp = 0.5 * sqrt((1.0 / (x ^ 3.0)));
	else
		tmp = 1.0 / (x ^ 1.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.7], N[(N[Power[x, -0.5], $MachinePrecision] + N[(-1.0 / N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+102], N[(0.5 * N[Sqrt[N[(1.0 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[Power[x, 1.5], $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 150000000:\\ \;\;\;\;{x}^{-0.5} - {\left(1 + x\right)}^{-0.5}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;0.5 \cdot \sqrt{\frac{1}{{x}^{3}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{x}^{1.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 150000000.0)
   (- (pow x -0.5) (pow (+ 1.0 x) -0.5))
   (if (<= x 5.6e+102)
     (* 0.5 (sqrt (/ 1.0 (pow x 3.0))))
     (/ 1.0 (pow x 1.5)))))

C

double code(double x) {
	double tmp;
	if (x <= 150000000.0) {
		tmp = pow(x, -0.5) - pow((1.0 + x), -0.5);
	} else if (x <= 5.6e+102) {
		tmp = 0.5 * sqrt((1.0 / pow(x, 3.0)));
	} else {
		tmp = 1.0 / pow(x, 1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 150000000.0d0) then
        tmp = (x ** (-0.5d0)) - ((1.0d0 + x) ** (-0.5d0))
    else if (x <= 5.6d+102) then
        tmp = 0.5d0 * sqrt((1.0d0 / (x ** 3.0d0)))
    else
        tmp = 1.0d0 / (x ** 1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 150000000.0) {
		tmp = Math.pow(x, -0.5) - Math.pow((1.0 + x), -0.5);
	} else if (x <= 5.6e+102) {
		tmp = 0.5 * Math.sqrt((1.0 / Math.pow(x, 3.0)));
	} else {
		tmp = 1.0 / Math.pow(x, 1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 150000000.0:
		tmp = math.pow(x, -0.5) - math.pow((1.0 + x), -0.5)
	elif x <= 5.6e+102:
		tmp = 0.5 * math.sqrt((1.0 / math.pow(x, 3.0)))
	else:
		tmp = 1.0 / math.pow(x, 1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 150000000.0)
		tmp = Float64((x ^ -0.5) - (Float64(1.0 + x) ^ -0.5));
	elseif (x <= 5.6e+102)
		tmp = Float64(0.5 * sqrt(Float64(1.0 / (x ^ 3.0))));
	else
		tmp = Float64(1.0 / (x ^ 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 150000000.0)
		tmp = (x ^ -0.5) - ((1.0 + x) ^ -0.5);
	elseif (x <= 5.6e+102)
		tmp = 0.5 * sqrt((1.0 / (x ^ 3.0)));
	else
		tmp = 1.0 / (x ^ 1.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 150000000.0], N[(N[Power[x, -0.5], $MachinePrecision] - N[Power[N[(1.0 + x), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+102], N[(0.5 * N[Sqrt[N[(1.0 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[Power[x, 1.5], $MachinePrecision]), $MachinePrecision]]]

Derivation

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Alternative 4: 71.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2:\\ \;\;\;\;{x}^{-0.5} + \frac{-1}{1 + x \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{x}^{1.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 3.2)
   (+ (pow x -0.5) (/ -1.0 (+ 1.0 (* x 0.5))))
   (/ 1.0 (pow x 1.5))))

C

double code(double x) {
	double tmp;
	if (x <= 3.2) {
		tmp = pow(x, -0.5) + (-1.0 / (1.0 + (x * 0.5)));
	} else {
		tmp = 1.0 / pow(x, 1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 3.2d0) then
        tmp = (x ** (-0.5d0)) + ((-1.0d0) / (1.0d0 + (x * 0.5d0)))
    else
        tmp = 1.0d0 / (x ** 1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 3.2) {
		tmp = Math.pow(x, -0.5) + (-1.0 / (1.0 + (x * 0.5)));
	} else {
		tmp = 1.0 / Math.pow(x, 1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 3.2:
		tmp = math.pow(x, -0.5) + (-1.0 / (1.0 + (x * 0.5)))
	else:
		tmp = 1.0 / math.pow(x, 1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 3.2)
		tmp = Float64((x ^ -0.5) + Float64(-1.0 / Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = Float64(1.0 / (x ^ 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 3.2)
		tmp = (x ^ -0.5) + (-1.0 / (1.0 + (x * 0.5)));
	else
		tmp = 1.0 / (x ^ 1.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 3.2], N[(N[Power[x, -0.5], $MachinePrecision] + N[(-1.0 / N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[Power[x, 1.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 71.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45:\\ \;\;\;\;{x}^{-0.5} - \left(1 + x \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{x}^{1.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.45) (- (pow x -0.5) (+ 1.0 (* x -0.5))) (/ 1.0 (pow x 1.5))))

C

double code(double x) {
	double tmp;
	if (x <= 1.45) {
		tmp = pow(x, -0.5) - (1.0 + (x * -0.5));
	} else {
		tmp = 1.0 / pow(x, 1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.45d0) then
        tmp = (x ** (-0.5d0)) - (1.0d0 + (x * (-0.5d0)))
    else
        tmp = 1.0d0 / (x ** 1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.45) {
		tmp = Math.pow(x, -0.5) - (1.0 + (x * -0.5));
	} else {
		tmp = 1.0 / Math.pow(x, 1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.45:
		tmp = math.pow(x, -0.5) - (1.0 + (x * -0.5))
	else:
		tmp = 1.0 / math.pow(x, 1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.45)
		tmp = Float64((x ^ -0.5) - Float64(1.0 + Float64(x * -0.5)));
	else
		tmp = Float64(1.0 / (x ^ 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.45)
		tmp = (x ^ -0.5) - (1.0 + (x * -0.5));
	else
		tmp = 1.0 / (x ^ 1.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.45], N[(N[Power[x, -0.5], $MachinePrecision] - N[(1.0 + N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[Power[x, 1.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 71.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.85:\\ \;\;\;\;{x}^{-0.5} + -1\\ \mathbf{else}:\\ \;\;\;\;{x}^{-1.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 0.85) (+ (pow x -0.5) -1.0) (pow x -1.5)))

C

double code(double x) {
	double tmp;
	if (x <= 0.85) {
		tmp = pow(x, -0.5) + -1.0;
	} else {
		tmp = pow(x, -1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.85d0) then
        tmp = (x ** (-0.5d0)) + (-1.0d0)
    else
        tmp = x ** (-1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.85) {
		tmp = Math.pow(x, -0.5) + -1.0;
	} else {
		tmp = Math.pow(x, -1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.85:
		tmp = math.pow(x, -0.5) + -1.0
	else:
		tmp = math.pow(x, -1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.85)
		tmp = Float64((x ^ -0.5) + -1.0);
	else
		tmp = x ^ -1.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.85)
		tmp = (x ^ -0.5) + -1.0;
	else
		tmp = x ^ -1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.85], N[(N[Power[x, -0.5], $MachinePrecision] + -1.0), $MachinePrecision], N[Power[x, -1.5], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 71.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.85:\\ \;\;\;\;{x}^{-0.5} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{x}^{1.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 0.85) (+ (pow x -0.5) -1.0) (/ 1.0 (pow x 1.5))))

C

double code(double x) {
	double tmp;
	if (x <= 0.85) {
		tmp = pow(x, -0.5) + -1.0;
	} else {
		tmp = 1.0 / pow(x, 1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.85d0) then
        tmp = (x ** (-0.5d0)) + (-1.0d0)
    else
        tmp = 1.0d0 / (x ** 1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.85) {
		tmp = Math.pow(x, -0.5) + -1.0;
	} else {
		tmp = 1.0 / Math.pow(x, 1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.85:
		tmp = math.pow(x, -0.5) + -1.0
	else:
		tmp = 1.0 / math.pow(x, 1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.85)
		tmp = Float64((x ^ -0.5) + -1.0);
	else
		tmp = Float64(1.0 / (x ^ 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.85)
		tmp = (x ^ -0.5) + -1.0;
	else
		tmp = 1.0 / (x ^ 1.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.85], N[(N[Power[x, -0.5], $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 / N[Power[x, 1.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 69.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;{x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;{x}^{-1.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.0) (pow x -0.5) (pow x -1.5)))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = pow(x, -0.5);
	} else {
		tmp = pow(x, -1.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = x ** (-0.5d0)
    else
        tmp = x ** (-1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = Math.pow(x, -0.5);
	} else {
		tmp = Math.pow(x, -1.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = math.pow(x, -0.5)
	else:
		tmp = math.pow(x, -1.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = x ^ -0.5;
	else
		tmp = x ^ -1.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = x ^ -0.5;
	else
		tmp = x ^ -1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[Power[x, -0.5], $MachinePrecision], N[Power[x, -1.5], $MachinePrecision]]

Derivation

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

Alternative 9: 24.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {x}^{-1.5} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (pow x -1.5))

C

double code(double x) {
	return pow(x, -1.5);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x ** (-1.5d0)
end function

Java

public static double code(double x) {
	return Math.pow(x, -1.5);
}

Python

def code(x):
	return math.pow(x, -1.5)

Julia

function code(x)
	return x ^ -1.5
end

MATLAB

function tmp = code(x)
	tmp = x ^ -1.5;
end

Wolfram

code[x_] := N[Power[x, -1.5], $MachinePrecision]

Derivation

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

Alternative 10: 2.3% accurate, 41.8× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + -1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ (* x 0.5) -1.0))

C

double code(double x) {
	return (x * 0.5) + -1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 0.5d0) + (-1.0d0)
end function

Java

public static double code(double x) {
	return (x * 0.5) + -1.0;
}

Python

def code(x):
	return (x * 0.5) + -1.0

Julia

function code(x)
	return Float64(Float64(x * 0.5) + -1.0)
end

MATLAB

function tmp = code(x)
	tmp = (x * 0.5) + -1.0;
end

Wolfram

code[x_] := N[(N[(x * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]

Derivation

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

Developer target: 98.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x) {
	return 1.0 / (((x + 1.0) * sqrt(x)) + (x * sqrt((x + 1.0))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / (((x + 1.0d0) * sqrt(x)) + (x * sqrt((x + 1.0d0))))
end function

Java

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

Python

def code(x):
	return 1.0 / (((x + 1.0) * math.sqrt(x)) + (x * math.sqrt((x + 1.0))))

Julia

function code(x)
	return Float64(1.0 / Float64(Float64(Float64(x + 1.0) * sqrt(x)) + Float64(x * sqrt(Float64(x + 1.0)))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / (((x + 1.0) * sqrt(x)) + (x * sqrt((x + 1.0))));
end

Wolfram

code[x_] := N[(1.0 / N[(N[(N[(x + 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(x * N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023343 
(FPCore (x)
  :name "2isqrt (example 3.6)"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ (* (+ x 1.0) (sqrt x)) (* x (sqrt (+ x 1.0)))))

  (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))