ABCF->ab-angle a

Percentage Accurate: 20.3% → 53.5%

Time: 30.6s

Alternatives: 17

Speedup: 3.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ \frac{-\sqrt{\left(2 \cdot \left(t_0 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (- (pow B 2.0) (* (* 4.0 A) C))))
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* t_0 F))
       (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
    t_0)))

C

double code(double A, double B, double C, double F) {
	double t_0 = pow(B, 2.0) - ((4.0 * A) * C);
	return -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / t_0;
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    t_0 = (b ** 2.0d0) - ((4.0d0 * a) * c)
    code = -sqrt(((2.0d0 * (t_0 * f)) * ((a + c) + sqrt((((a - c) ** 2.0d0) + (b ** 2.0d0)))))) / t_0
end function

Java

public static double code(double A, double B, double C, double F) {
	double t_0 = Math.pow(B, 2.0) - ((4.0 * A) * C);
	return -Math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / t_0;
}

Python

def code(A, B, C, F):
	t_0 = math.pow(B, 2.0) - ((4.0 * A) * C)
	return -math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / t_0

Julia

function code(A, B, C, F)
	t_0 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	return Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_0 * F)) * Float64(Float64(A + C) + sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0))))))) / t_0)
end

MATLAB

function tmp = code(A, B, C, F)
	t_0 = (B ^ 2.0) - ((4.0 * A) * C);
	tmp = -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / t_0;
end

Wolfram

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision]]

Initial Program: 20.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ \frac{-\sqrt{\left(2 \cdot \left(t_0 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (- (pow B 2.0) (* (* 4.0 A) C))))
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* t_0 F))
       (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
    t_0)))

C

double code(double A, double B, double C, double F) {
	double t_0 = pow(B, 2.0) - ((4.0 * A) * C);
	return -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / t_0;
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    t_0 = (b ** 2.0d0) - ((4.0d0 * a) * c)
    code = -sqrt(((2.0d0 * (t_0 * f)) * ((a + c) + sqrt((((a - c) ** 2.0d0) + (b ** 2.0d0)))))) / t_0
end function

Java

public static double code(double A, double B, double C, double F) {
	double t_0 = Math.pow(B, 2.0) - ((4.0 * A) * C);
	return -Math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / t_0;
}

Python

def code(A, B, C, F):
	t_0 = math.pow(B, 2.0) - ((4.0 * A) * C)
	return -math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / t_0

Julia

function code(A, B, C, F)
	t_0 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	return Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_0 * F)) * Float64(Float64(A + C) + sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0))))))) / t_0)
end

MATLAB

function tmp = code(A, B, C, F)
	t_0 = (B ^ 2.0) - ((4.0 * A) * C);
	tmp = -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / t_0;
end

Wolfram

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision]]

Alternative 1: 53.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;{B_m}^{2} \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \left(-\sqrt{A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)}\right)}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B_m, A\right)} \cdot \sqrt{F}\right) \cdot \left(\sqrt{2} \cdot \frac{-1}{B_m}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= (pow B_m 2.0) 5e+112)
   (/
    (*
     (sqrt (* 2.0 (* F (fma B_m B_m (* A (* C -4.0))))))
     (- (sqrt (+ A (+ C (hypot (- A C) B_m))))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (* (* (sqrt (+ A (hypot B_m A))) (sqrt F)) (* (sqrt 2.0) (/ -1.0 B_m)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (pow(B_m, 2.0) <= 5e+112) {
		tmp = (sqrt((2.0 * (F * fma(B_m, B_m, (A * (C * -4.0)))))) * -sqrt((A + (C + hypot((A - C), B_m))))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * (sqrt(2.0) * (-1.0 / B_m));
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if ((B_m ^ 2.0) <= 5e+112)
		tmp = Float64(Float64(sqrt(Float64(2.0 * Float64(F * fma(B_m, B_m, Float64(A * Float64(C * -4.0)))))) * Float64(-sqrt(Float64(A + Float64(C + hypot(Float64(A - C), B_m)))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	else
		tmp = Float64(Float64(sqrt(Float64(A + hypot(B_m, A))) * sqrt(F)) * Float64(sqrt(2.0) * Float64(-1.0 / B_m)));
	end
	return tmp
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 5e+112], N[(N[(N[Sqrt[N[(2.0 * N[(F * N[(B$95$m * B$95$m + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(-1.0 / B$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, -4 \cdot \left(A \cdot C\right)\right)\\ \mathbf{if}\;{B_m}^{2} \leq 10^{+98}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot t_0\right) \cdot \left(F \cdot \left(\mathsf{hypot}\left(A - C, B_m\right) + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B_m, A\right)} \cdot \sqrt{F}\right) \cdot \left(\sqrt{2} \cdot \frac{-1}{B_m}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (fma B_m B_m (* -4.0 (* A C)))))
   (if (<= (pow B_m 2.0) 1e+98)
     (/ (- (sqrt (* (* 2.0 t_0) (* F (+ (hypot (- A C) B_m) (+ A C)))))) t_0)
     (* (* (sqrt (+ A (hypot B_m A))) (sqrt F)) (* (sqrt 2.0) (/ -1.0 B_m))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = fma(B_m, B_m, (-4.0 * (A * C)));
	double tmp;
	if (pow(B_m, 2.0) <= 1e+98) {
		tmp = -sqrt(((2.0 * t_0) * (F * (hypot((A - C), B_m) + (A + C))))) / t_0;
	} else {
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * (sqrt(2.0) * (-1.0 / B_m));
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = fma(B_m, B_m, Float64(-4.0 * Float64(A * C)))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 1e+98)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * t_0) * Float64(F * Float64(hypot(Float64(A - C), B_m) + Float64(A + C)))))) / t_0);
	else
		tmp = Float64(Float64(sqrt(Float64(A + hypot(B_m, A))) * sqrt(F)) * Float64(sqrt(2.0) * Float64(-1.0 / B_m)));
	end
	return tmp
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = N[(B$95$m * B$95$m + N[(-4.0 * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e+98], N[((-N[Sqrt[N[(N[(2.0 * t$95$0), $MachinePrecision] * N[(F * N[(N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision] + N[(A + C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], N[(N[(N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(-1.0 / B$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 49.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;{B_m}^{2} \leq 10^{+98}:\\ \;\;\;\;\frac{-\sqrt{\left(t_0 \cdot \left(2 \cdot F\right)\right) \cdot \left(A + \left(C + \mathsf{hypot}\left(B_m, A - C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B_m, A\right)} \cdot \sqrt{F}\right) \cdot \left(\sqrt{2} \cdot \frac{-1}{B_m}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (fma B_m B_m (* A (* C -4.0)))))
   (if (<= (pow B_m 2.0) 1e+98)
     (/ (- (sqrt (* (* t_0 (* 2.0 F)) (+ A (+ C (hypot B_m (- A C))))))) t_0)
     (* (* (sqrt (+ A (hypot B_m A))) (sqrt F)) (* (sqrt 2.0) (/ -1.0 B_m))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = fma(B_m, B_m, (A * (C * -4.0)));
	double tmp;
	if (pow(B_m, 2.0) <= 1e+98) {
		tmp = -sqrt(((t_0 * (2.0 * F)) * (A + (C + hypot(B_m, (A - C)))))) / t_0;
	} else {
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * (sqrt(2.0) * (-1.0 / B_m));
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = fma(B_m, B_m, Float64(A * Float64(C * -4.0)))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 1e+98)
		tmp = Float64(Float64(-sqrt(Float64(Float64(t_0 * Float64(2.0 * F)) * Float64(A + Float64(C + hypot(B_m, Float64(A - C))))))) / t_0);
	else
		tmp = Float64(Float64(sqrt(Float64(A + hypot(B_m, A))) * sqrt(F)) * Float64(sqrt(2.0) * Float64(-1.0 / B_m)));
	end
	return tmp
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = N[(B$95$m * B$95$m + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e+98], N[((-N[Sqrt[N[(N[(t$95$0 * N[(2.0 * F), $MachinePrecision]), $MachinePrecision] * N[(A + N[(C + N[Sqrt[B$95$m ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], N[(N[(N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(-1.0 / B$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 45.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;B_m \leq 1.65 \cdot 10^{-78}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(-0.5 \cdot \frac{{B_m}^{2}}{A} + 2 \cdot C\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B_m, A\right)} \cdot \sqrt{F}\right) \cdot \left(\sqrt{2} \cdot \frac{-1}{B_m}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= B_m 1.65e-78)
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* -4.0 (* A (* C F))))
       (+ (* -0.5 (/ (pow B_m 2.0) A)) (* 2.0 C)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (* (* (sqrt (+ A (hypot B_m A))) (sqrt F)) (* (sqrt 2.0) (/ -1.0 B_m)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (B_m <= 1.65e-78) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (pow(B_m, 2.0) / A)) + (2.0 * C)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * (sqrt(2.0) * (-1.0 / B_m));
	}
	return tmp;
}

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (B_m <= 1.65e-78) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (Math.pow(B_m, 2.0) / A)) + (2.0 * C)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (Math.sqrt((A + Math.hypot(B_m, A))) * Math.sqrt(F)) * (Math.sqrt(2.0) * (-1.0 / B_m));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if B_m <= 1.65e-78:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (math.pow(B_m, 2.0) / A)) + (2.0 * C)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	else:
		tmp = (math.sqrt((A + math.hypot(B_m, A))) * math.sqrt(F)) * (math.sqrt(2.0) * (-1.0 / B_m))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (B_m <= 1.65e-78)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(-0.5 * Float64((B_m ^ 2.0) / A)) + Float64(2.0 * C))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	else
		tmp = Float64(Float64(sqrt(Float64(A + hypot(B_m, A))) * sqrt(F)) * Float64(sqrt(2.0) * Float64(-1.0 / B_m)));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (B_m <= 1.65e-78)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * ((B_m ^ 2.0) / A)) + (2.0 * C)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	else
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * (sqrt(2.0) * (-1.0 / B_m));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[B$95$m, 1.65e-78], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(-0.5 * N[(N[Power[B$95$m, 2.0], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision] + N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(-1.0 / B$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 45.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;B_m \leq 1.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(-0.5 \cdot \frac{{B_m}^{2}}{A} + 2 \cdot C\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B_m, A\right)} \cdot \sqrt{F}\right) \cdot \left(-\frac{\sqrt{2}}{B_m}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= B_m 1.7e-78)
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* -4.0 (* A (* C F))))
       (+ (* -0.5 (/ (pow B_m 2.0) A)) (* 2.0 C)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (* (* (sqrt (+ A (hypot B_m A))) (sqrt F)) (- (/ (sqrt 2.0) B_m)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (B_m <= 1.7e-78) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (pow(B_m, 2.0) / A)) + (2.0 * C)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * -(sqrt(2.0) / B_m);
	}
	return tmp;
}

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (B_m <= 1.7e-78) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (Math.pow(B_m, 2.0) / A)) + (2.0 * C)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (Math.sqrt((A + Math.hypot(B_m, A))) * Math.sqrt(F)) * -(Math.sqrt(2.0) / B_m);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if B_m <= 1.7e-78:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (math.pow(B_m, 2.0) / A)) + (2.0 * C)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	else:
		tmp = (math.sqrt((A + math.hypot(B_m, A))) * math.sqrt(F)) * -(math.sqrt(2.0) / B_m)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (B_m <= 1.7e-78)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(-0.5 * Float64((B_m ^ 2.0) / A)) + Float64(2.0 * C))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	else
		tmp = Float64(Float64(sqrt(Float64(A + hypot(B_m, A))) * sqrt(F)) * Float64(-Float64(sqrt(2.0) / B_m)));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (B_m <= 1.7e-78)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * ((B_m ^ 2.0) / A)) + (2.0 * C)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	else
		tmp = (sqrt((A + hypot(B_m, A))) * sqrt(F)) * -(sqrt(2.0) / B_m);
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[B$95$m, 1.7e-78], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(-0.5 * N[(N[Power[B$95$m, 2.0], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision] + N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * (-N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision])), $MachinePrecision]]

Derivation

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

Alternative 6: 42.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;B_m \leq 10^{-80}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(-0.5 \cdot \frac{{B_m}^{2}}{A} + 2 \cdot C\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;B_m \leq 6.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)\right)}}{B_m}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\sqrt{2}}{B_m}\right) \cdot \left(\sqrt{F} \cdot \sqrt{B_m + A}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= B_m 1e-80)
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* -4.0 (* A (* C F))))
       (+ (* -0.5 (/ (pow B_m 2.0) A)) (* 2.0 C)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (if (<= B_m 6.8e+87)
     (/ (- (sqrt (* 2.0 (* F (+ A (hypot B_m A)))))) B_m)
     (* (- (/ (sqrt 2.0) B_m)) (* (sqrt F) (sqrt (+ B_m A)))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (B_m <= 1e-80) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (pow(B_m, 2.0) / A)) + (2.0 * C)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (B_m <= 6.8e+87) {
		tmp = -sqrt((2.0 * (F * (A + hypot(B_m, A))))) / B_m;
	} else {
		tmp = -(sqrt(2.0) / B_m) * (sqrt(F) * sqrt((B_m + A)));
	}
	return tmp;
}

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (B_m <= 1e-80) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (Math.pow(B_m, 2.0) / A)) + (2.0 * C)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (B_m <= 6.8e+87) {
		tmp = -Math.sqrt((2.0 * (F * (A + Math.hypot(B_m, A))))) / B_m;
	} else {
		tmp = -(Math.sqrt(2.0) / B_m) * (Math.sqrt(F) * Math.sqrt((B_m + A)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if B_m <= 1e-80:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * (math.pow(B_m, 2.0) / A)) + (2.0 * C)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	elif B_m <= 6.8e+87:
		tmp = -math.sqrt((2.0 * (F * (A + math.hypot(B_m, A))))) / B_m
	else:
		tmp = -(math.sqrt(2.0) / B_m) * (math.sqrt(F) * math.sqrt((B_m + A)))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (B_m <= 1e-80)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(-0.5 * Float64((B_m ^ 2.0) / A)) + Float64(2.0 * C))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	elseif (B_m <= 6.8e+87)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(F * Float64(A + hypot(B_m, A)))))) / B_m);
	else
		tmp = Float64(Float64(-Float64(sqrt(2.0) / B_m)) * Float64(sqrt(F) * sqrt(Float64(B_m + A))));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (B_m <= 1e-80)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((-0.5 * ((B_m ^ 2.0) / A)) + (2.0 * C)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	elseif (B_m <= 6.8e+87)
		tmp = -sqrt((2.0 * (F * (A + hypot(B_m, A))))) / B_m;
	else
		tmp = -(sqrt(2.0) / B_m) * (sqrt(F) * sqrt((B_m + A)));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[B$95$m, 1e-80], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(-0.5 * N[(N[Power[B$95$m, 2.0], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision] + N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B$95$m, 6.8e+87], N[((-N[Sqrt[N[(2.0 * N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / B$95$m), $MachinePrecision], N[((-N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision]) * N[(N[Sqrt[F], $MachinePrecision] * N[Sqrt[N[(B$95$m + A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 7: 42.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := {B_m}^{2} - C \cdot \left(A \cdot 4\right)\\ \mathbf{if}\;B_m \leq 9 \cdot 10^{-81}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot C\right) \cdot \left(2 \cdot \left(F \cdot t_0\right)\right)}}{t_0}\\ \mathbf{elif}\;B_m \leq 1.45 \cdot 10^{+88}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)\right)}}{B_m}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\sqrt{2}}{B_m}\right) \cdot \left(\sqrt{F} \cdot \sqrt{B_m + A}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (- (pow B_m 2.0) (* C (* A 4.0)))))
   (if (<= B_m 9e-81)
     (/ (- (sqrt (* (* 2.0 C) (* 2.0 (* F t_0))))) t_0)
     (if (<= B_m 1.45e+88)
       (/ (- (sqrt (* 2.0 (* F (+ A (hypot B_m A)))))) B_m)
       (* (- (/ (sqrt 2.0) B_m)) (* (sqrt F) (sqrt (+ B_m A))))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = pow(B_m, 2.0) - (C * (A * 4.0));
	double tmp;
	if (B_m <= 9e-81) {
		tmp = -sqrt(((2.0 * C) * (2.0 * (F * t_0)))) / t_0;
	} else if (B_m <= 1.45e+88) {
		tmp = -sqrt((2.0 * (F * (A + hypot(B_m, A))))) / B_m;
	} else {
		tmp = -(sqrt(2.0) / B_m) * (sqrt(F) * sqrt((B_m + A)));
	}
	return tmp;
}

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double t_0 = Math.pow(B_m, 2.0) - (C * (A * 4.0));
	double tmp;
	if (B_m <= 9e-81) {
		tmp = -Math.sqrt(((2.0 * C) * (2.0 * (F * t_0)))) / t_0;
	} else if (B_m <= 1.45e+88) {
		tmp = -Math.sqrt((2.0 * (F * (A + Math.hypot(B_m, A))))) / B_m;
	} else {
		tmp = -(Math.sqrt(2.0) / B_m) * (Math.sqrt(F) * Math.sqrt((B_m + A)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = math.pow(B_m, 2.0) - (C * (A * 4.0))
	tmp = 0
	if B_m <= 9e-81:
		tmp = -math.sqrt(((2.0 * C) * (2.0 * (F * t_0)))) / t_0
	elif B_m <= 1.45e+88:
		tmp = -math.sqrt((2.0 * (F * (A + math.hypot(B_m, A))))) / B_m
	else:
		tmp = -(math.sqrt(2.0) / B_m) * (math.sqrt(F) * math.sqrt((B_m + A)))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0)))
	tmp = 0.0
	if (B_m <= 9e-81)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * C) * Float64(2.0 * Float64(F * t_0))))) / t_0);
	elseif (B_m <= 1.45e+88)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(F * Float64(A + hypot(B_m, A)))))) / B_m);
	else
		tmp = Float64(Float64(-Float64(sqrt(2.0) / B_m)) * Float64(sqrt(F) * sqrt(Float64(B_m + A))));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = (B_m ^ 2.0) - (C * (A * 4.0));
	tmp = 0.0;
	if (B_m <= 9e-81)
		tmp = -sqrt(((2.0 * C) * (2.0 * (F * t_0)))) / t_0;
	elseif (B_m <= 1.45e+88)
		tmp = -sqrt((2.0 * (F * (A + hypot(B_m, A))))) / B_m;
	else
		tmp = -(sqrt(2.0) / B_m) * (sqrt(F) * sqrt((B_m + A)));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B$95$m, 9e-81], N[((-N[Sqrt[N[(N[(2.0 * C), $MachinePrecision] * N[(2.0 * N[(F * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[B$95$m, 1.45e+88], N[((-N[Sqrt[N[(2.0 * N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / B$95$m), $MachinePrecision], N[((-N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision]) * N[(N[Sqrt[F], $MachinePrecision] * N[Sqrt[N[(B$95$m + A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 35.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{\sqrt{2}}{B_m}\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{+31}:\\ \;\;\;\;t_0 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2}}{\frac{A}{F}}}\right)\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+111}:\\ \;\;\;\;t_0 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{B_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\sqrt{2 \cdot A} \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (sqrt 2.0) B_m)))
   (if (<= A -9.5e+31)
     (* t_0 (- (sqrt (* -0.5 (/ (pow B_m 2.0) (/ A F))))))
     (if (<= A 3.8e+111)
       (* t_0 (* (sqrt F) (- (sqrt B_m))))
       (* t_0 (* (sqrt (* 2.0 A)) (- (sqrt F))))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = sqrt(2.0) / B_m;
	double tmp;
	if (A <= -9.5e+31) {
		tmp = t_0 * -sqrt((-0.5 * (pow(B_m, 2.0) / (A / F))));
	} else if (A <= 3.8e+111) {
		tmp = t_0 * (sqrt(F) * -sqrt(B_m));
	} else {
		tmp = t_0 * (sqrt((2.0 * A)) * -sqrt(F));
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(2.0d0) / b_m
    if (a <= (-9.5d+31)) then
        tmp = t_0 * -sqrt(((-0.5d0) * ((b_m ** 2.0d0) / (a / f))))
    else if (a <= 3.8d+111) then
        tmp = t_0 * (sqrt(f) * -sqrt(b_m))
    else
        tmp = t_0 * (sqrt((2.0d0 * a)) * -sqrt(f))
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double t_0 = Math.sqrt(2.0) / B_m;
	double tmp;
	if (A <= -9.5e+31) {
		tmp = t_0 * -Math.sqrt((-0.5 * (Math.pow(B_m, 2.0) / (A / F))));
	} else if (A <= 3.8e+111) {
		tmp = t_0 * (Math.sqrt(F) * -Math.sqrt(B_m));
	} else {
		tmp = t_0 * (Math.sqrt((2.0 * A)) * -Math.sqrt(F));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = math.sqrt(2.0) / B_m
	tmp = 0
	if A <= -9.5e+31:
		tmp = t_0 * -math.sqrt((-0.5 * (math.pow(B_m, 2.0) / (A / F))))
	elif A <= 3.8e+111:
		tmp = t_0 * (math.sqrt(F) * -math.sqrt(B_m))
	else:
		tmp = t_0 * (math.sqrt((2.0 * A)) * -math.sqrt(F))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(sqrt(2.0) / B_m)
	tmp = 0.0
	if (A <= -9.5e+31)
		tmp = Float64(t_0 * Float64(-sqrt(Float64(-0.5 * Float64((B_m ^ 2.0) / Float64(A / F))))));
	elseif (A <= 3.8e+111)
		tmp = Float64(t_0 * Float64(sqrt(F) * Float64(-sqrt(B_m))));
	else
		tmp = Float64(t_0 * Float64(sqrt(Float64(2.0 * A)) * Float64(-sqrt(F))));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = sqrt(2.0) / B_m;
	tmp = 0.0;
	if (A <= -9.5e+31)
		tmp = t_0 * -sqrt((-0.5 * ((B_m ^ 2.0) / (A / F))));
	elseif (A <= 3.8e+111)
		tmp = t_0 * (sqrt(F) * -sqrt(B_m));
	else
		tmp = t_0 * (sqrt((2.0 * A)) * -sqrt(F));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision]}, If[LessEqual[A, -9.5e+31], N[(t$95$0 * (-N[Sqrt[N[(-0.5 * N[(N[Power[B$95$m, 2.0], $MachinePrecision] / N[(A / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[A, 3.8e+111], N[(t$95$0 * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[B$95$m], $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[Sqrt[N[(2.0 * A), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[F], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 9: 41.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2}}{B_m} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{B_m}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -5e-310)
   (/ (sqrt (- F)) (sqrt A))
   (* (/ (sqrt 2.0) B_m) (* (sqrt F) (- (sqrt B_m))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = sqrt(-F) / sqrt(A);
	} else {
		tmp = (sqrt(2.0) / B_m) * (sqrt(F) * -sqrt(B_m));
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: tmp
    if (f <= (-5d-310)) then
        tmp = sqrt(-f) / sqrt(a)
    else
        tmp = (sqrt(2.0d0) / b_m) * (sqrt(f) * -sqrt(b_m))
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = Math.sqrt(-F) / Math.sqrt(A);
	} else {
		tmp = (Math.sqrt(2.0) / B_m) * (Math.sqrt(F) * -Math.sqrt(B_m));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if F <= -5e-310:
		tmp = math.sqrt(-F) / math.sqrt(A)
	else:
		tmp = (math.sqrt(2.0) / B_m) * (math.sqrt(F) * -math.sqrt(B_m))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (F <= -5e-310)
		tmp = Float64(sqrt(Float64(-F)) / sqrt(A));
	else
		tmp = Float64(Float64(sqrt(2.0) / B_m) * Float64(sqrt(F) * Float64(-sqrt(B_m))));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (F <= -5e-310)
		tmp = sqrt(-F) / sqrt(A);
	else
		tmp = (sqrt(2.0) / B_m) * (sqrt(F) * -sqrt(B_m));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[F, -5e-310], N[(N[Sqrt[(-F)], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[B$95$m], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 43.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \mathbf{elif}\;F \leq 1.96 \cdot 10^{+27}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)\right)}}{B_m}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B_m}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -5e-310)
   (/ (sqrt (- F)) (sqrt A))
   (if (<= F 1.96e+27)
     (/ (- (sqrt (* 2.0 (* F (+ A (hypot B_m A)))))) B_m)
     (* (sqrt (/ F B_m)) (- (sqrt 2.0))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = sqrt(-F) / sqrt(A);
	} else if (F <= 1.96e+27) {
		tmp = -sqrt((2.0 * (F * (A + hypot(B_m, A))))) / B_m;
	} else {
		tmp = sqrt((F / B_m)) * -sqrt(2.0);
	}
	return tmp;
}

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = Math.sqrt(-F) / Math.sqrt(A);
	} else if (F <= 1.96e+27) {
		tmp = -Math.sqrt((2.0 * (F * (A + Math.hypot(B_m, A))))) / B_m;
	} else {
		tmp = Math.sqrt((F / B_m)) * -Math.sqrt(2.0);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if F <= -5e-310:
		tmp = math.sqrt(-F) / math.sqrt(A)
	elif F <= 1.96e+27:
		tmp = -math.sqrt((2.0 * (F * (A + math.hypot(B_m, A))))) / B_m
	else:
		tmp = math.sqrt((F / B_m)) * -math.sqrt(2.0)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (F <= -5e-310)
		tmp = Float64(sqrt(Float64(-F)) / sqrt(A));
	elseif (F <= 1.96e+27)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(F * Float64(A + hypot(B_m, A)))))) / B_m);
	else
		tmp = Float64(sqrt(Float64(F / B_m)) * Float64(-sqrt(2.0)));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (F <= -5e-310)
		tmp = sqrt(-F) / sqrt(A);
	elseif (F <= 1.96e+27)
		tmp = -sqrt((2.0 * (F * (A + hypot(B_m, A))))) / B_m;
	else
		tmp = sqrt((F / B_m)) * -sqrt(2.0);
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[F, -5e-310], N[(N[Sqrt[(-F)], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.96e+27], N[((-N[Sqrt[N[(2.0 * N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / B$95$m), $MachinePrecision], N[(N[Sqrt[N[(F / B$95$m), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]]

Derivation

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

Alternative 11: 39.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \mathbf{elif}\;F \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\left(-\frac{\sqrt{2}}{B_m}\right) \cdot \sqrt{B_m \cdot F}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B_m}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -5e-310)
   (/ (sqrt (- F)) (sqrt A))
   (if (<= F 1.5e-113)
     (* (- (/ (sqrt 2.0) B_m)) (sqrt (* B_m F)))
     (* (sqrt (/ F B_m)) (- (sqrt 2.0))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = sqrt(-F) / sqrt(A);
	} else if (F <= 1.5e-113) {
		tmp = -(sqrt(2.0) / B_m) * sqrt((B_m * F));
	} else {
		tmp = sqrt((F / B_m)) * -sqrt(2.0);
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: tmp
    if (f <= (-5d-310)) then
        tmp = sqrt(-f) / sqrt(a)
    else if (f <= 1.5d-113) then
        tmp = -(sqrt(2.0d0) / b_m) * sqrt((b_m * f))
    else
        tmp = sqrt((f / b_m)) * -sqrt(2.0d0)
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = Math.sqrt(-F) / Math.sqrt(A);
	} else if (F <= 1.5e-113) {
		tmp = -(Math.sqrt(2.0) / B_m) * Math.sqrt((B_m * F));
	} else {
		tmp = Math.sqrt((F / B_m)) * -Math.sqrt(2.0);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if F <= -5e-310:
		tmp = math.sqrt(-F) / math.sqrt(A)
	elif F <= 1.5e-113:
		tmp = -(math.sqrt(2.0) / B_m) * math.sqrt((B_m * F))
	else:
		tmp = math.sqrt((F / B_m)) * -math.sqrt(2.0)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (F <= -5e-310)
		tmp = Float64(sqrt(Float64(-F)) / sqrt(A));
	elseif (F <= 1.5e-113)
		tmp = Float64(Float64(-Float64(sqrt(2.0) / B_m)) * sqrt(Float64(B_m * F)));
	else
		tmp = Float64(sqrt(Float64(F / B_m)) * Float64(-sqrt(2.0)));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (F <= -5e-310)
		tmp = sqrt(-F) / sqrt(A);
	elseif (F <= 1.5e-113)
		tmp = -(sqrt(2.0) / B_m) * sqrt((B_m * F));
	else
		tmp = sqrt((F / B_m)) * -sqrt(2.0);
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[F, -5e-310], N[(N[Sqrt[(-F)], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.5e-113], N[((-N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision]) * N[Sqrt[N[(B$95$m * F), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(F / B$95$m), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]]

Derivation

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

Alternative 12: 14.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \sqrt{\frac{-F}{C}}\\ \mathbf{if}\;C \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{A \cdot F} \cdot \frac{-2}{B_m}\\ \mathbf{elif}\;C \leq 0.1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (sqrt (/ (- F) C))))
   (if (<= C -2.7e+91)
     t_0
     (if (<= C 2.2e-154)
       (* (sqrt (* A F)) (/ (- 2.0) B_m))
       (if (<= C 0.1) t_0 (/ (sqrt (- F)) (sqrt A)))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = sqrt((-F / C));
	double tmp;
	if (C <= -2.7e+91) {
		tmp = t_0;
	} else if (C <= 2.2e-154) {
		tmp = sqrt((A * F)) * (-2.0 / B_m);
	} else if (C <= 0.1) {
		tmp = t_0;
	} else {
		tmp = sqrt(-F) / sqrt(A);
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt((-f / c))
    if (c <= (-2.7d+91)) then
        tmp = t_0
    else if (c <= 2.2d-154) then
        tmp = sqrt((a * f)) * (-2.0d0 / b_m)
    else if (c <= 0.1d0) then
        tmp = t_0
    else
        tmp = sqrt(-f) / sqrt(a)
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double t_0 = Math.sqrt((-F / C));
	double tmp;
	if (C <= -2.7e+91) {
		tmp = t_0;
	} else if (C <= 2.2e-154) {
		tmp = Math.sqrt((A * F)) * (-2.0 / B_m);
	} else if (C <= 0.1) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt(-F) / Math.sqrt(A);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = math.sqrt((-F / C))
	tmp = 0
	if C <= -2.7e+91:
		tmp = t_0
	elif C <= 2.2e-154:
		tmp = math.sqrt((A * F)) * (-2.0 / B_m)
	elif C <= 0.1:
		tmp = t_0
	else:
		tmp = math.sqrt(-F) / math.sqrt(A)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = sqrt(Float64(Float64(-F) / C))
	tmp = 0.0
	if (C <= -2.7e+91)
		tmp = t_0;
	elseif (C <= 2.2e-154)
		tmp = Float64(sqrt(Float64(A * F)) * Float64(Float64(-2.0) / B_m));
	elseif (C <= 0.1)
		tmp = t_0;
	else
		tmp = Float64(sqrt(Float64(-F)) / sqrt(A));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = sqrt((-F / C));
	tmp = 0.0;
	if (C <= -2.7e+91)
		tmp = t_0;
	elseif (C <= 2.2e-154)
		tmp = sqrt((A * F)) * (-2.0 / B_m);
	elseif (C <= 0.1)
		tmp = t_0;
	else
		tmp = sqrt(-F) / sqrt(A);
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = N[Sqrt[N[((-F) / C), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[C, -2.7e+91], t$95$0, If[LessEqual[C, 2.2e-154], N[(N[Sqrt[N[(A * F), $MachinePrecision]], $MachinePrecision] * N[((-2.0) / B$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 0.1], t$95$0, N[(N[Sqrt[(-F)], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 13: 33.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B_m}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -5e-310)
   (/ (sqrt (- F)) (sqrt A))
   (* (sqrt (/ F B_m)) (- (sqrt 2.0)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = sqrt(-F) / sqrt(A);
	} else {
		tmp = sqrt((F / B_m)) * -sqrt(2.0);
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: tmp
    if (f <= (-5d-310)) then
        tmp = sqrt(-f) / sqrt(a)
    else
        tmp = sqrt((f / b_m)) * -sqrt(2.0d0)
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -5e-310) {
		tmp = Math.sqrt(-F) / Math.sqrt(A);
	} else {
		tmp = Math.sqrt((F / B_m)) * -Math.sqrt(2.0);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if F <= -5e-310:
		tmp = math.sqrt(-F) / math.sqrt(A)
	else:
		tmp = math.sqrt((F / B_m)) * -math.sqrt(2.0)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (F <= -5e-310)
		tmp = Float64(sqrt(Float64(-F)) / sqrt(A));
	else
		tmp = Float64(sqrt(Float64(F / B_m)) * Float64(-sqrt(2.0)));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (F <= -5e-310)
		tmp = sqrt(-F) / sqrt(A);
	else
		tmp = sqrt((F / B_m)) * -sqrt(2.0);
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[F, -5e-310], N[(N[Sqrt[(-F)], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(F / B$95$m), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]

Derivation

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

Alternative 14: 13.9% accurate, 5.7× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \sqrt{\frac{-F}{C}}\\ \mathbf{if}\;C \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{A \cdot F} \cdot \frac{-2}{B_m}\\ \mathbf{elif}\;C \leq 3:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (sqrt (/ (- F) C))))
   (if (<= C -1.7e+88)
     t_0
     (if (<= C 2.5e-154)
       (* (sqrt (* A F)) (/ (- 2.0) B_m))
       (if (<= C 3.0) t_0 (sqrt (/ (- F) A)))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = sqrt((-F / C));
	double tmp;
	if (C <= -1.7e+88) {
		tmp = t_0;
	} else if (C <= 2.5e-154) {
		tmp = sqrt((A * F)) * (-2.0 / B_m);
	} else if (C <= 3.0) {
		tmp = t_0;
	} else {
		tmp = sqrt((-F / A));
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt((-f / c))
    if (c <= (-1.7d+88)) then
        tmp = t_0
    else if (c <= 2.5d-154) then
        tmp = sqrt((a * f)) * (-2.0d0 / b_m)
    else if (c <= 3.0d0) then
        tmp = t_0
    else
        tmp = sqrt((-f / a))
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double t_0 = Math.sqrt((-F / C));
	double tmp;
	if (C <= -1.7e+88) {
		tmp = t_0;
	} else if (C <= 2.5e-154) {
		tmp = Math.sqrt((A * F)) * (-2.0 / B_m);
	} else if (C <= 3.0) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt((-F / A));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = math.sqrt((-F / C))
	tmp = 0
	if C <= -1.7e+88:
		tmp = t_0
	elif C <= 2.5e-154:
		tmp = math.sqrt((A * F)) * (-2.0 / B_m)
	elif C <= 3.0:
		tmp = t_0
	else:
		tmp = math.sqrt((-F / A))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = sqrt(Float64(Float64(-F) / C))
	tmp = 0.0
	if (C <= -1.7e+88)
		tmp = t_0;
	elseif (C <= 2.5e-154)
		tmp = Float64(sqrt(Float64(A * F)) * Float64(Float64(-2.0) / B_m));
	elseif (C <= 3.0)
		tmp = t_0;
	else
		tmp = sqrt(Float64(Float64(-F) / A));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = sqrt((-F / C));
	tmp = 0.0;
	if (C <= -1.7e+88)
		tmp = t_0;
	elseif (C <= 2.5e-154)
		tmp = sqrt((A * F)) * (-2.0 / B_m);
	elseif (C <= 3.0)
		tmp = t_0;
	else
		tmp = sqrt((-F / A));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = N[Sqrt[N[((-F) / C), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[C, -1.7e+88], t$95$0, If[LessEqual[C, 2.5e-154], N[(N[Sqrt[N[(A * F), $MachinePrecision]], $MachinePrecision] * N[((-2.0) / B$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.0], t$95$0, N[Sqrt[N[((-F) / A), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

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

Alternative 15: 13.9% accurate, 6.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;C \leq 0.00057:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= C 0.00057) (sqrt (/ (- F) C)) (sqrt (/ (- F) A))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (C <= 0.00057) {
		tmp = sqrt((-F / C));
	} else {
		tmp = sqrt((-F / A));
	}
	return tmp;
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: tmp
    if (c <= 0.00057d0) then
        tmp = sqrt((-f / c))
    else
        tmp = sqrt((-f / a))
    end if
    code = tmp
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	double tmp;
	if (C <= 0.00057) {
		tmp = Math.sqrt((-F / C));
	} else {
		tmp = Math.sqrt((-F / A));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if C <= 0.00057:
		tmp = math.sqrt((-F / C))
	else:
		tmp = math.sqrt((-F / A))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (C <= 0.00057)
		tmp = sqrt(Float64(Float64(-F) / C));
	else
		tmp = sqrt(Float64(Float64(-F) / A));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	tmp = 0.0;
	if (C <= 0.00057)
		tmp = sqrt((-F / C));
	else
		tmp = sqrt((-F / A));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[C, 0.00057], N[Sqrt[N[((-F) / C), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[((-F) / A), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 16: 11.5% accurate, 6.1× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \sqrt{\frac{-F}{A}} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F) :precision binary64 (sqrt (/ (- F) A)))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	return sqrt((-F / A));
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    code = sqrt((-f / a))
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	return Math.sqrt((-F / A));
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	return math.sqrt((-F / A))

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	return sqrt(Float64(Float64(-F) / A))
end

MATLAB

B_m = abs(B);
function tmp = code(A, B_m, C, F)
	tmp = sqrt((-F / A));
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := N[Sqrt[N[((-F) / A), $MachinePrecision]], $MachinePrecision]

Derivation

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

Alternative 17: 1.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \sqrt{\frac{F}{A}} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F) :precision binary64 (sqrt (/ F A)))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	return sqrt((F / A));
}

Fortran

B_m = abs(B)
real(8) function code(a, b_m, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    code = sqrt((f / a))
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	return Math.sqrt((F / A));
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	return math.sqrt((F / A))

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	return sqrt(Float64(F / A))
end

MATLAB

B_m = abs(B);
function tmp = code(A, B_m, C, F)
	tmp = sqrt((F / A));
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := N[Sqrt[N[(F / A), $MachinePrecision]], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024003 
(FPCore (A B C F)
  :name "ABCF->ab-angle a"
  :precision binary64
  (/ (- (sqrt (* (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F)) (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))) (- (pow B 2.0) (* (* 4.0 A) C))))