ABCF->ab-angle a

Percentage Accurate: 18.9% → 52.4%

Time: 41.0s

Alternatives: 21

Speedup: 6.0×

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: 18.9% 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: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;{B_m}^{2} \leq 5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{C + \mathsf{hypot}\left(B_m, C\right)} \cdot \sqrt{F}\right) \cdot \frac{-1}{\frac{B_m}{\sqrt{2}}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= (pow B_m 2.0) 5e+166)
   (/
    (*
     (sqrt (+ A (+ C (hypot (- A C) B_m))))
     (- (sqrt (* 2.0 (* F (fma B_m B_m (* A (* C -4.0))))))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (* (* (sqrt (+ C (hypot B_m C))) (sqrt F)) (/ -1.0 (/ B_m (sqrt 2.0))))))

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+166) {
		tmp = (sqrt((A + (C + hypot((A - C), B_m)))) * -sqrt((2.0 * (F * fma(B_m, B_m, (A * (C * -4.0))))))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (sqrt((C + hypot(B_m, C))) * sqrt(F)) * (-1.0 / (B_m / sqrt(2.0)));
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if ((B_m ^ 2.0) <= 5e+166)
		tmp = Float64(Float64(sqrt(Float64(A + Float64(C + hypot(Float64(A - C), B_m)))) * Float64(-sqrt(Float64(2.0 * Float64(F * fma(B_m, B_m, Float64(A * Float64(C * -4.0)))))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	else
		tmp = Float64(Float64(sqrt(Float64(C + hypot(B_m, C))) * sqrt(F)) * Float64(-1.0 / Float64(B_m / sqrt(2.0))));
	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+166], N[(N[(N[Sqrt[N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-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])), $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[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(B$95$m / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \frac{\sqrt{2}}{B_m}\\ t_2 := {B_m}^{2} - C \cdot \left(A \cdot 4\right)\\ \mathbf{if}\;{B_m}^{2} \leq 10^{-220}:\\ \;\;\;\;\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(2 \cdot C\right)} \cdot \frac{-1}{t_0}\\ \mathbf{elif}\;{B_m}^{2} \leq 5 \cdot 10^{-122}:\\ \;\;\;\;t_1 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2}}{\frac{C}{F}}}\right)\\ \mathbf{elif}\;{B_m}^{2} \leq 20000000000:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot C\right) \cdot \left(2 \cdot \left(F \cdot t_2\right)\right)}}{t_2}\\ \mathbf{elif}\;{B_m}^{2} \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t_1 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2} \cdot F}{C}}\right)\\ \mathbf{elif}\;{B_m}^{2} \leq 10^{+65}:\\ \;\;\;\;\frac{-\sqrt{2}}{B_m} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(B_m, A\right)}\right)\right)\\ \end{array} \end{array} \]

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))))
        (t_1 (/ (sqrt 2.0) B_m))
        (t_2 (- (pow B_m 2.0) (* C (* A 4.0)))))
   (if (<= (pow B_m 2.0) 1e-220)
     (* (sqrt (* (* 2.0 (* F t_0)) (* 2.0 C))) (/ -1.0 t_0))
     (if (<= (pow B_m 2.0) 5e-122)
       (* t_1 (- (sqrt (* -0.5 (/ (pow B_m 2.0) (/ C F))))))
       (if (<= (pow B_m 2.0) 20000000000.0)
         (/ (- (sqrt (* (* 2.0 C) (* 2.0 (* F t_2))))) t_2)
         (if (<= (pow B_m 2.0) 5e+16)
           (* t_1 (- (sqrt (* -0.5 (/ (* (pow B_m 2.0) F) C)))))
           (if (<= (pow B_m 2.0) 1e+65)
             (* (/ (- (sqrt 2.0)) B_m) (sqrt (* F (+ C (hypot B_m C)))))
             (* t_1 (* (sqrt F) (- (sqrt (+ A (hypot B_m A)))))))))))))

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 t_1 = sqrt(2.0) / B_m;
	double t_2 = pow(B_m, 2.0) - (C * (A * 4.0));
	double tmp;
	if (pow(B_m, 2.0) <= 1e-220) {
		tmp = sqrt(((2.0 * (F * t_0)) * (2.0 * C))) * (-1.0 / t_0);
	} else if (pow(B_m, 2.0) <= 5e-122) {
		tmp = t_1 * -sqrt((-0.5 * (pow(B_m, 2.0) / (C / F))));
	} else if (pow(B_m, 2.0) <= 20000000000.0) {
		tmp = -sqrt(((2.0 * C) * (2.0 * (F * t_2)))) / t_2;
	} else if (pow(B_m, 2.0) <= 5e+16) {
		tmp = t_1 * -sqrt((-0.5 * ((pow(B_m, 2.0) * F) / C)));
	} else if (pow(B_m, 2.0) <= 1e+65) {
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	} else {
		tmp = t_1 * (sqrt(F) * -sqrt((A + hypot(B_m, A))));
	}
	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)))
	t_1 = Float64(sqrt(2.0) / B_m)
	t_2 = Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0)))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 1e-220)
		tmp = Float64(sqrt(Float64(Float64(2.0 * Float64(F * t_0)) * Float64(2.0 * C))) * Float64(-1.0 / t_0));
	elseif ((B_m ^ 2.0) <= 5e-122)
		tmp = Float64(t_1 * Float64(-sqrt(Float64(-0.5 * Float64((B_m ^ 2.0) / Float64(C / F))))));
	elseif ((B_m ^ 2.0) <= 20000000000.0)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * C) * Float64(2.0 * Float64(F * t_2))))) / t_2);
	elseif ((B_m ^ 2.0) <= 5e+16)
		tmp = Float64(t_1 * Float64(-sqrt(Float64(-0.5 * Float64(Float64((B_m ^ 2.0) * F) / C)))));
	elseif ((B_m ^ 2.0) <= 1e+65)
		tmp = Float64(Float64(Float64(-sqrt(2.0)) / B_m) * sqrt(Float64(F * Float64(C + hypot(B_m, C)))));
	else
		tmp = Float64(t_1 * Float64(sqrt(F) * Float64(-sqrt(Float64(A + hypot(B_m, A))))));
	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]}, Block[{t$95$1 = N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e-220], N[(N[Sqrt[N[(N[(2.0 * N[(F * t$95$0), $MachinePrecision]), $MachinePrecision] * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 5e-122], N[(t$95$1 * (-N[Sqrt[N[(-0.5 * N[(N[Power[B$95$m, 2.0], $MachinePrecision] / N[(C / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 20000000000.0], N[((-N[Sqrt[N[(N[(2.0 * C), $MachinePrecision] * N[(2.0 * N[(F * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$2), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 5e+16], N[(t$95$1 * (-N[Sqrt[N[(-0.5 * N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] * F), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e+65], N[(N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision] * N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 3: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;{B_m}^{2} \leq 10^{-220}:\\ \;\;\;\;\frac{-\sqrt{\left(t_0 \cdot \left(2 \cdot F\right)\right) \cdot \left(A + \left(C + \mathsf{hypot}\left(B_m, A - C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;{B_m}^{2} \leq 2 \cdot 10^{-180}:\\ \;\;\;\;\left(\sqrt{F} \cdot \sqrt{\frac{{B_m}^{2}}{C} \cdot -0.5}\right) \cdot \frac{-\sqrt{2}}{B_m}\\ \mathbf{elif}\;{B_m}^{2} \leq 4 \cdot 10^{+151}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot t_0\right) \cdot \left(\left(A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)\right) \cdot F\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{C + \mathsf{hypot}\left(B_m, C\right)} \cdot \sqrt{F}\right) \cdot \frac{-1}{\frac{B_m}{\sqrt{2}}}\\ \end{array} \end{array} \]

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-220)
     (/ (- (sqrt (* (* t_0 (* 2.0 F)) (+ A (+ C (hypot B_m (- A C))))))) t_0)
     (if (<= (pow B_m 2.0) 2e-180)
       (*
        (* (sqrt F) (sqrt (* (/ (pow B_m 2.0) C) -0.5)))
        (/ (- (sqrt 2.0)) B_m))
       (if (<= (pow B_m 2.0) 4e+151)
         (/
          (- (sqrt (* (* 2.0 t_0) (* (+ A (+ C (hypot (- A C) B_m))) F))))
          t_0)
         (*
          (* (sqrt (+ C (hypot B_m C))) (sqrt F))
          (/ -1.0 (/ B_m (sqrt 2.0)))))))))

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-220) {
		tmp = -sqrt(((t_0 * (2.0 * F)) * (A + (C + hypot(B_m, (A - C)))))) / t_0;
	} else if (pow(B_m, 2.0) <= 2e-180) {
		tmp = (sqrt(F) * sqrt(((pow(B_m, 2.0) / C) * -0.5))) * (-sqrt(2.0) / B_m);
	} else if (pow(B_m, 2.0) <= 4e+151) {
		tmp = -sqrt(((2.0 * t_0) * ((A + (C + hypot((A - C), B_m))) * F))) / t_0;
	} else {
		tmp = (sqrt((C + hypot(B_m, C))) * sqrt(F)) * (-1.0 / (B_m / sqrt(2.0)));
	}
	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-220)
		tmp = Float64(Float64(-sqrt(Float64(Float64(t_0 * Float64(2.0 * F)) * Float64(A + Float64(C + hypot(B_m, Float64(A - C))))))) / t_0);
	elseif ((B_m ^ 2.0) <= 2e-180)
		tmp = Float64(Float64(sqrt(F) * sqrt(Float64(Float64((B_m ^ 2.0) / C) * -0.5))) * Float64(Float64(-sqrt(2.0)) / B_m));
	elseif ((B_m ^ 2.0) <= 4e+151)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * t_0) * Float64(Float64(A + Float64(C + hypot(Float64(A - C), B_m))) * F)))) / t_0);
	else
		tmp = Float64(Float64(sqrt(Float64(C + hypot(B_m, C))) * sqrt(F)) * Float64(-1.0 / Float64(B_m / sqrt(2.0))));
	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-220], 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], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 2e-180], N[(N[(N[Sqrt[F], $MachinePrecision] * N[Sqrt[N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 4e+151], N[((-N[Sqrt[N[(N[(2.0 * t$95$0), $MachinePrecision] * N[(N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * F), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], N[(N[(N[Sqrt[N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(B$95$m / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 4: 40.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(2 \cdot C + A \cdot 0\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{if}\;{B_m}^{2} \leq 5 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;{B_m}^{2} \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-\sqrt{2}}{B_m} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)}\\ \mathbf{elif}\;{B_m}^{2} \leq 20000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;{B_m}^{2} \leq 10^{+50}:\\ \;\;\;\;\frac{\sqrt{2}}{B_m} \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2} \cdot F}{C}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{\frac{1}{B_m}}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0
         (/
          (- (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ (* 2.0 C) (* A 0.0)))))
          (- (pow B_m 2.0) (* C (* A 4.0))))))
   (if (<= (pow B_m 2.0) 5e-197)
     t_0
     (if (<= (pow B_m 2.0) 5e-27)
       (* (/ (- (sqrt 2.0)) B_m) (sqrt (* F (+ C (hypot B_m C)))))
       (if (<= (pow B_m 2.0) 20000000000.0)
         t_0
         (if (<= (pow B_m 2.0) 1e+50)
           (* (/ (sqrt 2.0) B_m) (- (sqrt (* -0.5 (/ (* (pow B_m 2.0) F) C)))))
           (* (sqrt 2.0) (* (sqrt F) (- (sqrt (/ 1.0 B_m)))))))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	double tmp;
	if (pow(B_m, 2.0) <= 5e-197) {
		tmp = t_0;
	} else if (pow(B_m, 2.0) <= 5e-27) {
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	} else if (pow(B_m, 2.0) <= 20000000000.0) {
		tmp = t_0;
	} else if (pow(B_m, 2.0) <= 1e+50) {
		tmp = (sqrt(2.0) / B_m) * -sqrt((-0.5 * ((pow(B_m, 2.0) * F) / C)));
	} else {
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((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 t_0 = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	double tmp;
	if (Math.pow(B_m, 2.0) <= 5e-197) {
		tmp = t_0;
	} else if (Math.pow(B_m, 2.0) <= 5e-27) {
		tmp = (-Math.sqrt(2.0) / B_m) * Math.sqrt((F * (C + Math.hypot(B_m, C))));
	} else if (Math.pow(B_m, 2.0) <= 20000000000.0) {
		tmp = t_0;
	} else if (Math.pow(B_m, 2.0) <= 1e+50) {
		tmp = (Math.sqrt(2.0) / B_m) * -Math.sqrt((-0.5 * ((Math.pow(B_m, 2.0) * F) / C)));
	} else {
		tmp = Math.sqrt(2.0) * (Math.sqrt(F) * -Math.sqrt((1.0 / B_m)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	tmp = 0
	if math.pow(B_m, 2.0) <= 5e-197:
		tmp = t_0
	elif math.pow(B_m, 2.0) <= 5e-27:
		tmp = (-math.sqrt(2.0) / B_m) * math.sqrt((F * (C + math.hypot(B_m, C))))
	elif math.pow(B_m, 2.0) <= 20000000000.0:
		tmp = t_0
	elif math.pow(B_m, 2.0) <= 1e+50:
		tmp = (math.sqrt(2.0) / B_m) * -math.sqrt((-0.5 * ((math.pow(B_m, 2.0) * F) / C)))
	else:
		tmp = math.sqrt(2.0) * (math.sqrt(F) * -math.sqrt((1.0 / B_m)))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(2.0 * C) + Float64(A * 0.0))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 5e-197)
		tmp = t_0;
	elseif ((B_m ^ 2.0) <= 5e-27)
		tmp = Float64(Float64(Float64(-sqrt(2.0)) / B_m) * sqrt(Float64(F * Float64(C + hypot(B_m, C)))));
	elseif ((B_m ^ 2.0) <= 20000000000.0)
		tmp = t_0;
	elseif ((B_m ^ 2.0) <= 1e+50)
		tmp = Float64(Float64(sqrt(2.0) / B_m) * Float64(-sqrt(Float64(-0.5 * Float64(Float64((B_m ^ 2.0) * F) / C)))));
	else
		tmp = Float64(sqrt(2.0) * Float64(sqrt(F) * Float64(-sqrt(Float64(1.0 / B_m)))));
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	tmp = 0.0;
	if ((B_m ^ 2.0) <= 5e-197)
		tmp = t_0;
	elseif ((B_m ^ 2.0) <= 5e-27)
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	elseif ((B_m ^ 2.0) <= 20000000000.0)
		tmp = t_0;
	elseif ((B_m ^ 2.0) <= 1e+50)
		tmp = (sqrt(2.0) / B_m) * -sqrt((-0.5 * (((B_m ^ 2.0) * F) / C)));
	else
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((1.0 / B_m)));
	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[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(2.0 * C), $MachinePrecision] + N[(A * 0.0), $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[N[Power[B$95$m, 2.0], $MachinePrecision], 5e-197], t$95$0, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 5e-27], N[(N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision] * N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 20000000000.0], t$95$0, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e+50], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision] * (-N[Sqrt[N[(-0.5 * N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] * F), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(1.0 / B$95$m), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 40.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{\sqrt{2}}{B_m}\\ \mathbf{if}\;{B_m}^{2} \leq 5 \cdot 10^{-197}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(2 \cdot C + A \cdot 0\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;{B_m}^{2} \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\frac{-\sqrt{2}}{B_m} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)}\\ \mathbf{elif}\;{B_m}^{2} \leq 2000000000:\\ \;\;\;\;t_0 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2}}{\frac{A}{F}}}\right)\\ \mathbf{elif}\;{B_m}^{2} \leq 10^{+50}:\\ \;\;\;\;t_0 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2} \cdot F}{C}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{\frac{1}{B_m}}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (sqrt 2.0) B_m)))
   (if (<= (pow B_m 2.0) 5e-197)
     (/
      (- (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ (* 2.0 C) (* A 0.0)))))
      (- (pow B_m 2.0) (* C (* A 4.0))))
     (if (<= (pow B_m 2.0) 2e-9)
       (* (/ (- (sqrt 2.0)) B_m) (sqrt (* F (+ C (hypot B_m C)))))
       (if (<= (pow B_m 2.0) 2000000000.0)
         (* t_0 (- (sqrt (* -0.5 (/ (pow B_m 2.0) (/ A F))))))
         (if (<= (pow B_m 2.0) 1e+50)
           (* t_0 (- (sqrt (* -0.5 (/ (* (pow B_m 2.0) F) C)))))
           (* (sqrt 2.0) (* (sqrt F) (- (sqrt (/ 1.0 B_m)))))))))))

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 (pow(B_m, 2.0) <= 5e-197) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (pow(B_m, 2.0) <= 2e-9) {
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	} else if (pow(B_m, 2.0) <= 2000000000.0) {
		tmp = t_0 * -sqrt((-0.5 * (pow(B_m, 2.0) / (A / F))));
	} else if (pow(B_m, 2.0) <= 1e+50) {
		tmp = t_0 * -sqrt((-0.5 * ((pow(B_m, 2.0) * F) / C)));
	} else {
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((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 t_0 = Math.sqrt(2.0) / B_m;
	double tmp;
	if (Math.pow(B_m, 2.0) <= 5e-197) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (Math.pow(B_m, 2.0) <= 2e-9) {
		tmp = (-Math.sqrt(2.0) / B_m) * Math.sqrt((F * (C + Math.hypot(B_m, C))));
	} else if (Math.pow(B_m, 2.0) <= 2000000000.0) {
		tmp = t_0 * -Math.sqrt((-0.5 * (Math.pow(B_m, 2.0) / (A / F))));
	} else if (Math.pow(B_m, 2.0) <= 1e+50) {
		tmp = t_0 * -Math.sqrt((-0.5 * ((Math.pow(B_m, 2.0) * F) / C)));
	} else {
		tmp = Math.sqrt(2.0) * (Math.sqrt(F) * -Math.sqrt((1.0 / B_m)));
	}
	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 math.pow(B_m, 2.0) <= 5e-197:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	elif math.pow(B_m, 2.0) <= 2e-9:
		tmp = (-math.sqrt(2.0) / B_m) * math.sqrt((F * (C + math.hypot(B_m, C))))
	elif math.pow(B_m, 2.0) <= 2000000000.0:
		tmp = t_0 * -math.sqrt((-0.5 * (math.pow(B_m, 2.0) / (A / F))))
	elif math.pow(B_m, 2.0) <= 1e+50:
		tmp = t_0 * -math.sqrt((-0.5 * ((math.pow(B_m, 2.0) * F) / C)))
	else:
		tmp = math.sqrt(2.0) * (math.sqrt(F) * -math.sqrt((1.0 / B_m)))
	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 ((B_m ^ 2.0) <= 5e-197)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(2.0 * C) + Float64(A * 0.0))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	elseif ((B_m ^ 2.0) <= 2e-9)
		tmp = Float64(Float64(Float64(-sqrt(2.0)) / B_m) * sqrt(Float64(F * Float64(C + hypot(B_m, C)))));
	elseif ((B_m ^ 2.0) <= 2000000000.0)
		tmp = Float64(t_0 * Float64(-sqrt(Float64(-0.5 * Float64((B_m ^ 2.0) / Float64(A / F))))));
	elseif ((B_m ^ 2.0) <= 1e+50)
		tmp = Float64(t_0 * Float64(-sqrt(Float64(-0.5 * Float64(Float64((B_m ^ 2.0) * F) / C)))));
	else
		tmp = Float64(sqrt(2.0) * Float64(sqrt(F) * Float64(-sqrt(Float64(1.0 / B_m)))));
	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 ((B_m ^ 2.0) <= 5e-197)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	elseif ((B_m ^ 2.0) <= 2e-9)
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	elseif ((B_m ^ 2.0) <= 2000000000.0)
		tmp = t_0 * -sqrt((-0.5 * ((B_m ^ 2.0) / (A / F))));
	elseif ((B_m ^ 2.0) <= 1e+50)
		tmp = t_0 * -sqrt((-0.5 * (((B_m ^ 2.0) * F) / C)));
	else
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((1.0 / B_m)));
	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[N[Power[B$95$m, 2.0], $MachinePrecision], 5e-197], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(2.0 * C), $MachinePrecision] + N[(A * 0.0), $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[N[Power[B$95$m, 2.0], $MachinePrecision], 2e-9], N[(N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision] * N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 2000000000.0], 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[N[Power[B$95$m, 2.0], $MachinePrecision], 1e+50], N[(t$95$0 * (-N[Sqrt[N[(-0.5 * N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] * F), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(1.0 / B$95$m), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;{B_m}^{2} \leq 4 \cdot 10^{+151}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot t_0\right) \cdot \left(\left(A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)\right) \cdot F\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{C + \mathsf{hypot}\left(B_m, C\right)} \cdot \sqrt{F}\right) \cdot \frac{-1}{\frac{B_m}{\sqrt{2}}}\\ \end{array} \end{array} \]

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) 4e+151)
     (/ (- (sqrt (* (* 2.0 t_0) (* (+ A (+ C (hypot (- A C) B_m))) F)))) t_0)
     (* (* (sqrt (+ C (hypot B_m C))) (sqrt F)) (/ -1.0 (/ B_m (sqrt 2.0)))))))

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) <= 4e+151) {
		tmp = -sqrt(((2.0 * t_0) * ((A + (C + hypot((A - C), B_m))) * F))) / t_0;
	} else {
		tmp = (sqrt((C + hypot(B_m, C))) * sqrt(F)) * (-1.0 / (B_m / sqrt(2.0)));
	}
	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) <= 4e+151)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * t_0) * Float64(Float64(A + Float64(C + hypot(Float64(A - C), B_m))) * F)))) / t_0);
	else
		tmp = Float64(Float64(sqrt(Float64(C + hypot(B_m, C))) * sqrt(F)) * Float64(-1.0 / Float64(B_m / sqrt(2.0))));
	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], 4e+151], N[((-N[Sqrt[N[(N[(2.0 * t$95$0), $MachinePrecision] * N[(N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * F), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], N[(N[(N[Sqrt[N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(B$95$m / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 7: 41.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;{B_m}^{2} \leq 5 \cdot 10^{-197}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(2 \cdot C + A \cdot 0\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;{B_m}^{2} \leq 10^{+57}:\\ \;\;\;\;\frac{-\sqrt{2}}{B_m} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{\frac{1}{B_m}}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= (pow B_m 2.0) 5e-197)
   (/
    (- (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ (* 2.0 C) (* A 0.0)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (if (<= (pow B_m 2.0) 1e+57)
     (* (/ (- (sqrt 2.0)) B_m) (sqrt (* F (+ C (hypot B_m C)))))
     (* (sqrt 2.0) (* (sqrt F) (- (sqrt (/ 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-197) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (pow(B_m, 2.0) <= 1e+57) {
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	} else {
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((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 (Math.pow(B_m, 2.0) <= 5e-197) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (Math.pow(B_m, 2.0) <= 1e+57) {
		tmp = (-Math.sqrt(2.0) / B_m) * Math.sqrt((F * (C + Math.hypot(B_m, C))));
	} else {
		tmp = Math.sqrt(2.0) * (Math.sqrt(F) * -Math.sqrt((1.0 / B_m)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if math.pow(B_m, 2.0) <= 5e-197:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	elif math.pow(B_m, 2.0) <= 1e+57:
		tmp = (-math.sqrt(2.0) / B_m) * math.sqrt((F * (C + math.hypot(B_m, C))))
	else:
		tmp = math.sqrt(2.0) * (math.sqrt(F) * -math.sqrt((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-197)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(2.0 * C) + Float64(A * 0.0))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	elseif ((B_m ^ 2.0) <= 1e+57)
		tmp = Float64(Float64(Float64(-sqrt(2.0)) / B_m) * sqrt(Float64(F * Float64(C + hypot(B_m, C)))));
	else
		tmp = Float64(sqrt(2.0) * Float64(sqrt(F) * Float64(-sqrt(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 ^ 2.0) <= 5e-197)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	elseif ((B_m ^ 2.0) <= 1e+57)
		tmp = (-sqrt(2.0) / B_m) * sqrt((F * (C + hypot(B_m, C))));
	else
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((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[N[Power[B$95$m, 2.0], $MachinePrecision], 5e-197], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(2.0 * C), $MachinePrecision] + N[(A * 0.0), $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[N[Power[B$95$m, 2.0], $MachinePrecision], 1e+57], N[(N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision] * N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(1.0 / B$95$m), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 47.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{\sqrt{2}}{B_m}\\ t_1 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := C + \mathsf{hypot}\left(B_m, C\right)\\ \mathbf{if}\;B_m \leq 8 \cdot 10^{-105}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)} \cdot \left(-\sqrt{-8 \cdot \left(F \cdot \left(A \cdot C\right)\right)}\right)}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;B_m \leq 6.2:\\ \;\;\;\;\frac{1}{\frac{t_1}{-\sqrt{\left(2 \cdot \left(F \cdot t_1\right)\right) \cdot t_2}}}\\ \mathbf{elif}\;B_m \leq 205000000:\\ \;\;\;\;t_0 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2} \cdot F}{C}}\right)\\ \mathbf{elif}\;B_m \leq 8.8 \cdot 10^{+248}:\\ \;\;\;\;\left(\sqrt{t_2} \cdot \sqrt{F}\right) \cdot \frac{-\sqrt{2}}{B_m}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(B_m, A\right)}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (sqrt 2.0) B_m))
        (t_1 (fma B_m B_m (* A (* C -4.0))))
        (t_2 (+ C (hypot B_m C))))
   (if (<= B_m 8e-105)
     (/
      (*
       (sqrt (+ A (+ C (hypot (- A C) B_m))))
       (- (sqrt (* -8.0 (* F (* A C))))))
      (- (pow B_m 2.0) (* C (* A 4.0))))
     (if (<= B_m 6.2)
       (/ 1.0 (/ t_1 (- (sqrt (* (* 2.0 (* F t_1)) t_2)))))
       (if (<= B_m 205000000.0)
         (* t_0 (- (sqrt (* -0.5 (/ (* (pow B_m 2.0) F) C)))))
         (if (<= B_m 8.8e+248)
           (* (* (sqrt t_2) (sqrt F)) (/ (- (sqrt 2.0)) B_m))
           (* t_0 (* (sqrt F) (- (sqrt (+ A (hypot B_m A))))))))))))

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 t_1 = fma(B_m, B_m, (A * (C * -4.0)));
	double t_2 = C + hypot(B_m, C);
	double tmp;
	if (B_m <= 8e-105) {
		tmp = (sqrt((A + (C + hypot((A - C), B_m)))) * -sqrt((-8.0 * (F * (A * C))))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (B_m <= 6.2) {
		tmp = 1.0 / (t_1 / -sqrt(((2.0 * (F * t_1)) * t_2)));
	} else if (B_m <= 205000000.0) {
		tmp = t_0 * -sqrt((-0.5 * ((pow(B_m, 2.0) * F) / C)));
	} else if (B_m <= 8.8e+248) {
		tmp = (sqrt(t_2) * sqrt(F)) * (-sqrt(2.0) / B_m);
	} else {
		tmp = t_0 * (sqrt(F) * -sqrt((A + hypot(B_m, A))));
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(sqrt(2.0) / B_m)
	t_1 = fma(B_m, B_m, Float64(A * Float64(C * -4.0)))
	t_2 = Float64(C + hypot(B_m, C))
	tmp = 0.0
	if (B_m <= 8e-105)
		tmp = Float64(Float64(sqrt(Float64(A + Float64(C + hypot(Float64(A - C), B_m)))) * Float64(-sqrt(Float64(-8.0 * Float64(F * Float64(A * C)))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	elseif (B_m <= 6.2)
		tmp = Float64(1.0 / Float64(t_1 / Float64(-sqrt(Float64(Float64(2.0 * Float64(F * t_1)) * t_2)))));
	elseif (B_m <= 205000000.0)
		tmp = Float64(t_0 * Float64(-sqrt(Float64(-0.5 * Float64(Float64((B_m ^ 2.0) * F) / C)))));
	elseif (B_m <= 8.8e+248)
		tmp = Float64(Float64(sqrt(t_2) * sqrt(F)) * Float64(Float64(-sqrt(2.0)) / B_m));
	else
		tmp = Float64(t_0 * Float64(sqrt(F) * Float64(-sqrt(Float64(A + hypot(B_m, A))))));
	end
	return 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]}, Block[{t$95$1 = N[(B$95$m * B$95$m + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B$95$m, 8e-105], N[(N[(N[Sqrt[N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(-8.0 * N[(F * N[(A * C), $MachinePrecision]), $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, 6.2], N[(1.0 / N[(t$95$1 / (-N[Sqrt[N[(N[(2.0 * N[(F * t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[B$95$m, 205000000.0], N[(t$95$0 * (-N[Sqrt[N[(-0.5 * N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] * F), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[B$95$m, 8.8e+248], N[(N[(N[Sqrt[t$95$2], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 9: 47.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{\sqrt{2}}{B_m}\\ t_1 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := C + \mathsf{hypot}\left(B_m, C\right)\\ \mathbf{if}\;B_m \leq 1.3 \cdot 10^{-103}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)} \cdot \left(-\sqrt{-8 \cdot \left(F \cdot \left(A \cdot C\right)\right)}\right)}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;B_m \leq 23.5:\\ \;\;\;\;\sqrt{\left(2 \cdot \left(F \cdot t_1\right)\right) \cdot t_2} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B_m \leq 205000000:\\ \;\;\;\;t_0 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2} \cdot F}{C}}\right)\\ \mathbf{elif}\;B_m \leq 9 \cdot 10^{+248}:\\ \;\;\;\;\left(\sqrt{t_2} \cdot \sqrt{F}\right) \cdot \frac{-\sqrt{2}}{B_m}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(B_m, A\right)}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (sqrt 2.0) B_m))
        (t_1 (fma B_m B_m (* A (* C -4.0))))
        (t_2 (+ C (hypot B_m C))))
   (if (<= B_m 1.3e-103)
     (/
      (*
       (sqrt (+ A (+ C (hypot (- A C) B_m))))
       (- (sqrt (* -8.0 (* F (* A C))))))
      (- (pow B_m 2.0) (* C (* A 4.0))))
     (if (<= B_m 23.5)
       (* (sqrt (* (* 2.0 (* F t_1)) t_2)) (/ -1.0 t_1))
       (if (<= B_m 205000000.0)
         (* t_0 (- (sqrt (* -0.5 (/ (* (pow B_m 2.0) F) C)))))
         (if (<= B_m 9e+248)
           (* (* (sqrt t_2) (sqrt F)) (/ (- (sqrt 2.0)) B_m))
           (* t_0 (* (sqrt F) (- (sqrt (+ A (hypot B_m A))))))))))))

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 t_1 = fma(B_m, B_m, (A * (C * -4.0)));
	double t_2 = C + hypot(B_m, C);
	double tmp;
	if (B_m <= 1.3e-103) {
		tmp = (sqrt((A + (C + hypot((A - C), B_m)))) * -sqrt((-8.0 * (F * (A * C))))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (B_m <= 23.5) {
		tmp = sqrt(((2.0 * (F * t_1)) * t_2)) * (-1.0 / t_1);
	} else if (B_m <= 205000000.0) {
		tmp = t_0 * -sqrt((-0.5 * ((pow(B_m, 2.0) * F) / C)));
	} else if (B_m <= 9e+248) {
		tmp = (sqrt(t_2) * sqrt(F)) * (-sqrt(2.0) / B_m);
	} else {
		tmp = t_0 * (sqrt(F) * -sqrt((A + hypot(B_m, A))));
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(sqrt(2.0) / B_m)
	t_1 = fma(B_m, B_m, Float64(A * Float64(C * -4.0)))
	t_2 = Float64(C + hypot(B_m, C))
	tmp = 0.0
	if (B_m <= 1.3e-103)
		tmp = Float64(Float64(sqrt(Float64(A + Float64(C + hypot(Float64(A - C), B_m)))) * Float64(-sqrt(Float64(-8.0 * Float64(F * Float64(A * C)))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	elseif (B_m <= 23.5)
		tmp = Float64(sqrt(Float64(Float64(2.0 * Float64(F * t_1)) * t_2)) * Float64(-1.0 / t_1));
	elseif (B_m <= 205000000.0)
		tmp = Float64(t_0 * Float64(-sqrt(Float64(-0.5 * Float64(Float64((B_m ^ 2.0) * F) / C)))));
	elseif (B_m <= 9e+248)
		tmp = Float64(Float64(sqrt(t_2) * sqrt(F)) * Float64(Float64(-sqrt(2.0)) / B_m));
	else
		tmp = Float64(t_0 * Float64(sqrt(F) * Float64(-sqrt(Float64(A + hypot(B_m, A))))));
	end
	return 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]}, Block[{t$95$1 = N[(B$95$m * B$95$m + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B$95$m, 1.3e-103], N[(N[(N[Sqrt[N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(-8.0 * N[(F * N[(A * C), $MachinePrecision]), $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, 23.5], N[(N[Sqrt[N[(N[(2.0 * N[(F * t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[B$95$m, 205000000.0], N[(t$95$0 * (-N[Sqrt[N[(-0.5 * N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] * F), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[B$95$m, 9e+248], N[(N[(N[Sqrt[t$95$2], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 10: 45.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := {B_m}^{2} - C \cdot \left(A \cdot 4\right)\\ t_1 := \frac{\sqrt{2}}{B_m}\\ \mathbf{if}\;B_m \leq 2.4 \cdot 10^{-99}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)} \cdot \left(-\sqrt{-8 \cdot \left(F \cdot \left(A \cdot C\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B_m \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)} \cdot \left(B_m \cdot \left(-\sqrt{2}\right)\right)}{t_0}\\ \mathbf{elif}\;B_m \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;t_1 \cdot \left(-\sqrt{-0.5 \cdot \frac{{B_m}^{2} \cdot F}{C}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(B_m, A\right)}\right)\right)\\ \end{array} \end{array} \]

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)))) (t_1 (/ (sqrt 2.0) B_m)))
   (if (<= B_m 2.4e-99)
     (/
      (*
       (sqrt (+ A (+ C (hypot (- A C) B_m))))
       (- (sqrt (* -8.0 (* F (* A C))))))
      t_0)
     (if (<= B_m 3.1e-15)
       (/ (* (sqrt (* F (+ C (hypot B_m C)))) (* B_m (- (sqrt 2.0)))) t_0)
       (if (<= B_m 3.5e+32)
         (* t_1 (- (sqrt (* -0.5 (/ (* (pow B_m 2.0) F) C)))))
         (* t_1 (* (sqrt F) (- (sqrt (+ A (hypot 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 t_1 = sqrt(2.0) / B_m;
	double tmp;
	if (B_m <= 2.4e-99) {
		tmp = (sqrt((A + (C + hypot((A - C), B_m)))) * -sqrt((-8.0 * (F * (A * C))))) / t_0;
	} else if (B_m <= 3.1e-15) {
		tmp = (sqrt((F * (C + hypot(B_m, C)))) * (B_m * -sqrt(2.0))) / t_0;
	} else if (B_m <= 3.5e+32) {
		tmp = t_1 * -sqrt((-0.5 * ((pow(B_m, 2.0) * F) / C)));
	} else {
		tmp = t_1 * (sqrt(F) * -sqrt((A + hypot(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 t_1 = Math.sqrt(2.0) / B_m;
	double tmp;
	if (B_m <= 2.4e-99) {
		tmp = (Math.sqrt((A + (C + Math.hypot((A - C), B_m)))) * -Math.sqrt((-8.0 * (F * (A * C))))) / t_0;
	} else if (B_m <= 3.1e-15) {
		tmp = (Math.sqrt((F * (C + Math.hypot(B_m, C)))) * (B_m * -Math.sqrt(2.0))) / t_0;
	} else if (B_m <= 3.5e+32) {
		tmp = t_1 * -Math.sqrt((-0.5 * ((Math.pow(B_m, 2.0) * F) / C)));
	} else {
		tmp = t_1 * (Math.sqrt(F) * -Math.sqrt((A + Math.hypot(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))
	t_1 = math.sqrt(2.0) / B_m
	tmp = 0
	if B_m <= 2.4e-99:
		tmp = (math.sqrt((A + (C + math.hypot((A - C), B_m)))) * -math.sqrt((-8.0 * (F * (A * C))))) / t_0
	elif B_m <= 3.1e-15:
		tmp = (math.sqrt((F * (C + math.hypot(B_m, C)))) * (B_m * -math.sqrt(2.0))) / t_0
	elif B_m <= 3.5e+32:
		tmp = t_1 * -math.sqrt((-0.5 * ((math.pow(B_m, 2.0) * F) / C)))
	else:
		tmp = t_1 * (math.sqrt(F) * -math.sqrt((A + math.hypot(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)))
	t_1 = Float64(sqrt(2.0) / B_m)
	tmp = 0.0
	if (B_m <= 2.4e-99)
		tmp = Float64(Float64(sqrt(Float64(A + Float64(C + hypot(Float64(A - C), B_m)))) * Float64(-sqrt(Float64(-8.0 * Float64(F * Float64(A * C)))))) / t_0);
	elseif (B_m <= 3.1e-15)
		tmp = Float64(Float64(sqrt(Float64(F * Float64(C + hypot(B_m, C)))) * Float64(B_m * Float64(-sqrt(2.0)))) / t_0);
	elseif (B_m <= 3.5e+32)
		tmp = Float64(t_1 * Float64(-sqrt(Float64(-0.5 * Float64(Float64((B_m ^ 2.0) * F) / C)))));
	else
		tmp = Float64(t_1 * Float64(sqrt(F) * Float64(-sqrt(Float64(A + hypot(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));
	t_1 = sqrt(2.0) / B_m;
	tmp = 0.0;
	if (B_m <= 2.4e-99)
		tmp = (sqrt((A + (C + hypot((A - C), B_m)))) * -sqrt((-8.0 * (F * (A * C))))) / t_0;
	elseif (B_m <= 3.1e-15)
		tmp = (sqrt((F * (C + hypot(B_m, C)))) * (B_m * -sqrt(2.0))) / t_0;
	elseif (B_m <= 3.5e+32)
		tmp = t_1 * -sqrt((-0.5 * (((B_m ^ 2.0) * F) / C)));
	else
		tmp = t_1 * (sqrt(F) * -sqrt((A + hypot(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]}, Block[{t$95$1 = N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision]}, If[LessEqual[B$95$m, 2.4e-99], N[(N[(N[Sqrt[N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(-8.0 * N[(F * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[B$95$m, 3.1e-15], N[(N[(N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(B$95$m * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[B$95$m, 3.5e+32], N[(t$95$1 * (-N[Sqrt[N[(-0.5 * N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] * F), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], N[(t$95$1 * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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1. Add Preprocessing

Alternative 11: 42.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{-\sqrt{2}}{B_m}\\ \mathbf{if}\;C \leq -1.28 \cdot 10^{+116}:\\ \;\;\;\;\left(\sqrt{F} \cdot \sqrt{\frac{{B_m}^{2}}{C} \cdot -0.5}\right) \cdot t_0\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-101}:\\ \;\;\;\;\frac{\sqrt{2}}{B_m} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(B_m, A\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{C + \mathsf{hypot}\left(B_m, C\right)} \cdot \sqrt{F}\right) \cdot t_0\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (- (sqrt 2.0)) B_m)))
   (if (<= C -1.28e+116)
     (* (* (sqrt F) (sqrt (* (/ (pow B_m 2.0) C) -0.5))) t_0)
     (if (<= C 1.15e-101)
       (* (/ (sqrt 2.0) B_m) (* (sqrt F) (- (sqrt (+ A (hypot B_m A))))))
       (* (* (sqrt (+ C (hypot B_m C))) (sqrt F)) t_0)))))

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 (C <= -1.28e+116) {
		tmp = (sqrt(F) * sqrt(((pow(B_m, 2.0) / C) * -0.5))) * t_0;
	} else if (C <= 1.15e-101) {
		tmp = (sqrt(2.0) / B_m) * (sqrt(F) * -sqrt((A + hypot(B_m, A))));
	} else {
		tmp = (sqrt((C + hypot(B_m, C))) * sqrt(F)) * t_0;
	}
	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.sqrt(2.0) / B_m;
	double tmp;
	if (C <= -1.28e+116) {
		tmp = (Math.sqrt(F) * Math.sqrt(((Math.pow(B_m, 2.0) / C) * -0.5))) * t_0;
	} else if (C <= 1.15e-101) {
		tmp = (Math.sqrt(2.0) / B_m) * (Math.sqrt(F) * -Math.sqrt((A + Math.hypot(B_m, A))));
	} else {
		tmp = (Math.sqrt((C + Math.hypot(B_m, C))) * Math.sqrt(F)) * t_0;
	}
	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 C <= -1.28e+116:
		tmp = (math.sqrt(F) * math.sqrt(((math.pow(B_m, 2.0) / C) * -0.5))) * t_0
	elif C <= 1.15e-101:
		tmp = (math.sqrt(2.0) / B_m) * (math.sqrt(F) * -math.sqrt((A + math.hypot(B_m, A))))
	else:
		tmp = (math.sqrt((C + math.hypot(B_m, C))) * math.sqrt(F)) * t_0
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(Float64(-sqrt(2.0)) / B_m)
	tmp = 0.0
	if (C <= -1.28e+116)
		tmp = Float64(Float64(sqrt(F) * sqrt(Float64(Float64((B_m ^ 2.0) / C) * -0.5))) * t_0);
	elseif (C <= 1.15e-101)
		tmp = Float64(Float64(sqrt(2.0) / B_m) * Float64(sqrt(F) * Float64(-sqrt(Float64(A + hypot(B_m, A))))));
	else
		tmp = Float64(Float64(sqrt(Float64(C + hypot(B_m, C))) * sqrt(F)) * t_0);
	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 (C <= -1.28e+116)
		tmp = (sqrt(F) * sqrt((((B_m ^ 2.0) / C) * -0.5))) * t_0;
	elseif (C <= 1.15e-101)
		tmp = (sqrt(2.0) / B_m) * (sqrt(F) * -sqrt((A + hypot(B_m, A))));
	else
		tmp = (sqrt((C + hypot(B_m, C))) * sqrt(F)) * t_0;
	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[C, -1.28e+116], N[(N[(N[Sqrt[F], $MachinePrecision] * N[Sqrt[N[(N[(N[Power[B$95$m, 2.0], $MachinePrecision] / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[C, 1.15e-101], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 12: 44.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\left(A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)\right) \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)} \cdot \frac{-1}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{C + \mathsf{hypot}\left(B_m, C\right)} \cdot \sqrt{F}\right) \cdot \frac{-\sqrt{2}}{B_m}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -5e-310)
   (*
    (sqrt (* (+ A (+ C (hypot (- A C) B_m))) (* -8.0 (* F (* A C)))))
    (/ -1.0 (- (pow B_m 2.0) (* C (* A 4.0)))))
   (* (* (sqrt (+ C (hypot B_m C))) (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 (F <= -5e-310) {
		tmp = sqrt(((A + (C + hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / (pow(B_m, 2.0) - (C * (A * 4.0))));
	} else {
		tmp = (sqrt((C + hypot(B_m, C))) * 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 (F <= -5e-310) {
		tmp = Math.sqrt(((A + (C + Math.hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / (Math.pow(B_m, 2.0) - (C * (A * 4.0))));
	} else {
		tmp = (Math.sqrt((C + Math.hypot(B_m, C))) * 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 F <= -5e-310:
		tmp = math.sqrt(((A + (C + math.hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / (math.pow(B_m, 2.0) - (C * (A * 4.0))))
	else:
		tmp = (math.sqrt((C + math.hypot(B_m, C))) * 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 (F <= -5e-310)
		tmp = Float64(sqrt(Float64(Float64(A + Float64(C + hypot(Float64(A - C), B_m))) * Float64(-8.0 * Float64(F * Float64(A * C))))) * Float64(-1.0 / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0)))));
	else
		tmp = Float64(Float64(sqrt(Float64(C + hypot(B_m, C))) * 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 (F <= -5e-310)
		tmp = sqrt(((A + (C + hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / ((B_m ^ 2.0) - (C * (A * 4.0))));
	else
		tmp = (sqrt((C + hypot(B_m, C))) * 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[F, -5e-310], N[(N[Sqrt[N[(N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-8.0 * N[(F * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 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 13: 40.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;{B_m}^{2} \leq 10000000:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(2 \cdot C + A \cdot 0\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{\frac{1}{B_m}}\right)\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= (pow B_m 2.0) 10000000.0)
   (/
    (- (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ (* 2.0 C) (* A 0.0)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (* (sqrt 2.0) (* (sqrt F) (- (sqrt (/ 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) <= 10000000.0) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((1.0 / 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 ((b_m ** 2.0d0) <= 10000000.0d0) then
        tmp = -sqrt(((2.0d0 * ((-4.0d0) * (a * (c * f)))) * ((2.0d0 * c) + (a * 0.0d0)))) / ((b_m ** 2.0d0) - (c * (a * 4.0d0)))
    else
        tmp = sqrt(2.0d0) * (sqrt(f) * -sqrt((1.0d0 / 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 (Math.pow(B_m, 2.0) <= 10000000.0) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = Math.sqrt(2.0) * (Math.sqrt(F) * -Math.sqrt((1.0 / B_m)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if math.pow(B_m, 2.0) <= 10000000.0:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	else:
		tmp = math.sqrt(2.0) * (math.sqrt(F) * -math.sqrt((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) <= 10000000.0)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(2.0 * C) + Float64(A * 0.0))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	else
		tmp = Float64(sqrt(2.0) * Float64(sqrt(F) * Float64(-sqrt(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 ^ 2.0) <= 10000000.0)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	else
		tmp = sqrt(2.0) * (sqrt(F) * -sqrt((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[N[Power[B$95$m, 2.0], $MachinePrecision], 10000000.0], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(2.0 * C), $MachinePrecision] + N[(A * 0.0), $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[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(1.0 / B$95$m), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 40.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;{B_m}^{2} \leq 10000000:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(2 \cdot C + A \cdot 0\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B_m}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= (pow B_m 2.0) 10000000.0)
   (/
    (- (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ (* 2.0 C) (* A 0.0)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (* (/ (sqrt F) (sqrt B_m)) (- (sqrt 2.0)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (pow(B_m, 2.0) <= 10000000.0) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (sqrt(F) / sqrt(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 ((b_m ** 2.0d0) <= 10000000.0d0) then
        tmp = -sqrt(((2.0d0 * ((-4.0d0) * (a * (c * f)))) * ((2.0d0 * c) + (a * 0.0d0)))) / ((b_m ** 2.0d0) - (c * (a * 4.0d0)))
    else
        tmp = (sqrt(f) / sqrt(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 (Math.pow(B_m, 2.0) <= 10000000.0) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else {
		tmp = (Math.sqrt(F) / Math.sqrt(B_m)) * -Math.sqrt(2.0);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if math.pow(B_m, 2.0) <= 10000000.0:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	else:
		tmp = (math.sqrt(F) / math.sqrt(B_m)) * -math.sqrt(2.0)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if ((B_m ^ 2.0) <= 10000000.0)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(Float64(2.0 * C) + Float64(A * 0.0))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	else
		tmp = Float64(Float64(sqrt(F) / sqrt(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 ((B_m ^ 2.0) <= 10000000.0)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * ((2.0 * C) + (A * 0.0)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	else
		tmp = (sqrt(F) / sqrt(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[N[Power[B$95$m, 2.0], $MachinePrecision], 10000000.0], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(2.0 * C), $MachinePrecision] + N[(A * 0.0), $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[F], $MachinePrecision] / N[Sqrt[B$95$m], $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]

Derivation

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

Alternative 15: 41.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := -\sqrt{2}\\ \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\left(A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)\right) \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)} \cdot \frac{-1}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;F \leq 3.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{t_0}{B_m} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B_m}} \cdot t_0\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (- (sqrt 2.0))))
   (if (<= F -5e-310)
     (*
      (sqrt (* (+ A (+ C (hypot (- A C) B_m))) (* -8.0 (* F (* A C)))))
      (/ -1.0 (- (pow B_m 2.0) (* C (* A 4.0)))))
     (if (<= F 3.1e+97)
       (* (/ t_0 B_m) (sqrt (* F (+ C (hypot B_m C)))))
       (* (/ (sqrt F) (sqrt B_m)) t_0)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = -sqrt(2.0);
	double tmp;
	if (F <= -5e-310) {
		tmp = sqrt(((A + (C + hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / (pow(B_m, 2.0) - (C * (A * 4.0))));
	} else if (F <= 3.1e+97) {
		tmp = (t_0 / B_m) * sqrt((F * (C + hypot(B_m, C))));
	} else {
		tmp = (sqrt(F) / sqrt(B_m)) * t_0;
	}
	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.sqrt(2.0);
	double tmp;
	if (F <= -5e-310) {
		tmp = Math.sqrt(((A + (C + Math.hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / (Math.pow(B_m, 2.0) - (C * (A * 4.0))));
	} else if (F <= 3.1e+97) {
		tmp = (t_0 / B_m) * Math.sqrt((F * (C + Math.hypot(B_m, C))));
	} else {
		tmp = (Math.sqrt(F) / Math.sqrt(B_m)) * t_0;
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = -math.sqrt(2.0)
	tmp = 0
	if F <= -5e-310:
		tmp = math.sqrt(((A + (C + math.hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / (math.pow(B_m, 2.0) - (C * (A * 4.0))))
	elif F <= 3.1e+97:
		tmp = (t_0 / B_m) * math.sqrt((F * (C + math.hypot(B_m, C))))
	else:
		tmp = (math.sqrt(F) / math.sqrt(B_m)) * t_0
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(-sqrt(2.0))
	tmp = 0.0
	if (F <= -5e-310)
		tmp = Float64(sqrt(Float64(Float64(A + Float64(C + hypot(Float64(A - C), B_m))) * Float64(-8.0 * Float64(F * Float64(A * C))))) * Float64(-1.0 / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0)))));
	elseif (F <= 3.1e+97)
		tmp = Float64(Float64(t_0 / B_m) * sqrt(Float64(F * Float64(C + hypot(B_m, C)))));
	else
		tmp = Float64(Float64(sqrt(F) / sqrt(B_m)) * t_0);
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = -sqrt(2.0);
	tmp = 0.0;
	if (F <= -5e-310)
		tmp = sqrt(((A + (C + hypot((A - C), B_m))) * (-8.0 * (F * (A * C))))) * (-1.0 / ((B_m ^ 2.0) - (C * (A * 4.0))));
	elseif (F <= 3.1e+97)
		tmp = (t_0 / B_m) * sqrt((F * (C + hypot(B_m, C))));
	else
		tmp = (sqrt(F) / sqrt(B_m)) * t_0;
	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[2.0], $MachinePrecision])}, If[LessEqual[F, -5e-310], N[(N[Sqrt[N[(N[(A + N[(C + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-8.0 * N[(F * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(C * N[(A * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 3.1e+97], N[(N[(t$95$0 / B$95$m), $MachinePrecision] * N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[F], $MachinePrecision] / N[Sqrt[B$95$m], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

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

Alternative 16: 38.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := -\sqrt{2}\\ t_1 := C + \mathsf{hypot}\left(B_m, C\right)\\ \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{t_1 \cdot \left(2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;F \leq 3.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{t_0}{B_m} \cdot \sqrt{F \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B_m}} \cdot t_0\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (- (sqrt 2.0))) (t_1 (+ C (hypot B_m C))))
   (if (<= F -5e-310)
     (*
      (sqrt (* t_1 (* 2.0 (* -4.0 (* F (* A C))))))
      (/ -1.0 (fma B_m B_m (* A (* C -4.0)))))
     (if (<= F 3.1e+97)
       (* (/ t_0 B_m) (sqrt (* F t_1)))
       (* (/ (sqrt F) (sqrt B_m)) t_0)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = -sqrt(2.0);
	double t_1 = C + hypot(B_m, C);
	double tmp;
	if (F <= -5e-310) {
		tmp = sqrt((t_1 * (2.0 * (-4.0 * (F * (A * C)))))) * (-1.0 / fma(B_m, B_m, (A * (C * -4.0))));
	} else if (F <= 3.1e+97) {
		tmp = (t_0 / B_m) * sqrt((F * t_1));
	} else {
		tmp = (sqrt(F) / sqrt(B_m)) * t_0;
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64(-sqrt(2.0))
	t_1 = Float64(C + hypot(B_m, C))
	tmp = 0.0
	if (F <= -5e-310)
		tmp = Float64(sqrt(Float64(t_1 * Float64(2.0 * Float64(-4.0 * Float64(F * Float64(A * C)))))) * Float64(-1.0 / fma(B_m, B_m, Float64(A * Float64(C * -4.0)))));
	elseif (F <= 3.1e+97)
		tmp = Float64(Float64(t_0 / B_m) * sqrt(Float64(F * t_1)));
	else
		tmp = Float64(Float64(sqrt(F) / sqrt(B_m)) * t_0);
	end
	return tmp
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := Block[{t$95$0 = (-N[Sqrt[2.0], $MachinePrecision])}, Block[{t$95$1 = N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -5e-310], N[(N[Sqrt[N[(t$95$1 * N[(2.0 * N[(-4.0 * N[(F * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / N[(B$95$m * B$95$m + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 3.1e+97], N[(N[(t$95$0 / B$95$m), $MachinePrecision] * N[Sqrt[N[(F * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[F], $MachinePrecision] / N[Sqrt[B$95$m], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]]]]]

Derivation

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

Alternative 17: 36.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-\frac{\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(A + \left(A + C\right)\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;F \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;\frac{\sqrt{2}}{B_m} \cdot \left(-\sqrt{B_m \cdot F}\right)\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{2 \cdot \frac{F}{B_m}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -5e-310)
   (-
    (/
     (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ A (+ A C))))
     (- (pow B_m 2.0) (* C (* A 4.0)))))
   (if (<= F 2.9e+67)
     (* (/ (sqrt 2.0) B_m) (- (sqrt (* B_m F))))
     (- (sqrt (* 2.0 (/ F 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(((2.0 * (-4.0 * (A * (C * F)))) * (A + (A + C)))) / (pow(B_m, 2.0) - (C * (A * 4.0))));
	} else if (F <= 2.9e+67) {
		tmp = (sqrt(2.0) / B_m) * -sqrt((B_m * F));
	} else {
		tmp = -sqrt((2.0 * (F / 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(((2.0d0 * ((-4.0d0) * (a * (c * f)))) * (a + (a + c)))) / ((b_m ** 2.0d0) - (c * (a * 4.0d0))))
    else if (f <= 2.9d+67) then
        tmp = (sqrt(2.0d0) / b_m) * -sqrt((b_m * f))
    else
        tmp = -sqrt((2.0d0 * (f / 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(((2.0 * (-4.0 * (A * (C * F)))) * (A + (A + C)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0))));
	} else if (F <= 2.9e+67) {
		tmp = (Math.sqrt(2.0) / B_m) * -Math.sqrt((B_m * F));
	} else {
		tmp = -Math.sqrt((2.0 * (F / 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(((2.0 * (-4.0 * (A * (C * F)))) * (A + (A + C)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0))))
	elif F <= 2.9e+67:
		tmp = (math.sqrt(2.0) / B_m) * -math.sqrt((B_m * F))
	else:
		tmp = -math.sqrt((2.0 * (F / 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(-Float64(sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(A + Float64(A + C)))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0)))));
	elseif (F <= 2.9e+67)
		tmp = Float64(Float64(sqrt(2.0) / B_m) * Float64(-sqrt(Float64(B_m * F))));
	else
		tmp = Float64(-sqrt(Float64(2.0 * Float64(F / 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(((2.0 * (-4.0 * (A * (C * F)))) * (A + (A + C)))) / ((B_m ^ 2.0) - (C * (A * 4.0))));
	elseif (F <= 2.9e+67)
		tmp = (sqrt(2.0) / B_m) * -sqrt((B_m * F));
	else
		tmp = -sqrt((2.0 * (F / 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[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(A + N[(A + 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[F, 2.9e+67], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision] * (-N[Sqrt[N[(B$95$m * F), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], (-N[Sqrt[N[(2.0 * N[(F / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])]]

Derivation

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

Alternative 18: 36.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq -3.3 \cdot 10^{-270}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \left(C + \left(A + C\right)\right)}}{{B_m}^{2} - C \cdot \left(A \cdot 4\right)}\\ \mathbf{elif}\;F \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{\sqrt{2}}{B_m} \cdot \left(-\sqrt{B_m \cdot F}\right)\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{2 \cdot \frac{F}{B_m}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F -3.3e-270)
   (/
    (- (sqrt (* (* 2.0 (* -4.0 (* A (* C F)))) (+ C (+ A C)))))
    (- (pow B_m 2.0) (* C (* A 4.0))))
   (if (<= F 1.2e+67)
     (* (/ (sqrt 2.0) B_m) (- (sqrt (* B_m F))))
     (- (sqrt (* 2.0 (/ F B_m)))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= -3.3e-270) {
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * (C + (A + C)))) / (pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (F <= 1.2e+67) {
		tmp = (sqrt(2.0) / B_m) * -sqrt((B_m * F));
	} else {
		tmp = -sqrt((2.0 * (F / 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 <= (-3.3d-270)) then
        tmp = -sqrt(((2.0d0 * ((-4.0d0) * (a * (c * f)))) * (c + (a + c)))) / ((b_m ** 2.0d0) - (c * (a * 4.0d0)))
    else if (f <= 1.2d+67) then
        tmp = (sqrt(2.0d0) / b_m) * -sqrt((b_m * f))
    else
        tmp = -sqrt((2.0d0 * (f / 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 <= -3.3e-270) {
		tmp = -Math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * (C + (A + C)))) / (Math.pow(B_m, 2.0) - (C * (A * 4.0)));
	} else if (F <= 1.2e+67) {
		tmp = (Math.sqrt(2.0) / B_m) * -Math.sqrt((B_m * F));
	} else {
		tmp = -Math.sqrt((2.0 * (F / B_m)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if F <= -3.3e-270:
		tmp = -math.sqrt(((2.0 * (-4.0 * (A * (C * F)))) * (C + (A + C)))) / (math.pow(B_m, 2.0) - (C * (A * 4.0)))
	elif F <= 1.2e+67:
		tmp = (math.sqrt(2.0) / B_m) * -math.sqrt((B_m * F))
	else:
		tmp = -math.sqrt((2.0 * (F / B_m)))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (F <= -3.3e-270)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(-4.0 * Float64(A * Float64(C * F)))) * Float64(C + Float64(A + C))))) / Float64((B_m ^ 2.0) - Float64(C * Float64(A * 4.0))));
	elseif (F <= 1.2e+67)
		tmp = Float64(Float64(sqrt(2.0) / B_m) * Float64(-sqrt(Float64(B_m * F))));
	else
		tmp = Float64(-sqrt(Float64(2.0 * Float64(F / 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 <= -3.3e-270)
		tmp = -sqrt(((2.0 * (-4.0 * (A * (C * F)))) * (C + (A + C)))) / ((B_m ^ 2.0) - (C * (A * 4.0)));
	elseif (F <= 1.2e+67)
		tmp = (sqrt(2.0) / B_m) * -sqrt((B_m * F));
	else
		tmp = -sqrt((2.0 * (F / B_m)));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[F, -3.3e-270], N[((-N[Sqrt[N[(N[(2.0 * N[(-4.0 * N[(A * N[(C * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(C + N[(A + 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[F, 1.2e+67], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision] * (-N[Sqrt[N[(B$95$m * F), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], (-N[Sqrt[N[(2.0 * N[(F / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])]]

Derivation

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Alternative 19: 33.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} \mathbf{if}\;F \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{\sqrt{2}}{B_m} \cdot \left(-\sqrt{B_m \cdot F}\right)\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{2 \cdot \frac{F}{B_m}}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (if (<= F 1.2e+67)
   (* (/ (sqrt 2.0) B_m) (- (sqrt (* B_m F))))
   (- (sqrt (* 2.0 (/ F B_m))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double tmp;
	if (F <= 1.2e+67) {
		tmp = (sqrt(2.0) / B_m) * -sqrt((B_m * F));
	} else {
		tmp = -sqrt((2.0 * (F / 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 <= 1.2d+67) then
        tmp = (sqrt(2.0d0) / b_m) * -sqrt((b_m * f))
    else
        tmp = -sqrt((2.0d0 * (f / 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 <= 1.2e+67) {
		tmp = (Math.sqrt(2.0) / B_m) * -Math.sqrt((B_m * F));
	} else {
		tmp = -Math.sqrt((2.0 * (F / B_m)));
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	tmp = 0
	if F <= 1.2e+67:
		tmp = (math.sqrt(2.0) / B_m) * -math.sqrt((B_m * F))
	else:
		tmp = -math.sqrt((2.0 * (F / B_m)))
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	tmp = 0.0
	if (F <= 1.2e+67)
		tmp = Float64(Float64(sqrt(2.0) / B_m) * Float64(-sqrt(Float64(B_m * F))));
	else
		tmp = Float64(-sqrt(Float64(2.0 * Float64(F / 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 <= 1.2e+67)
		tmp = (sqrt(2.0) / B_m) * -sqrt((B_m * F));
	else
		tmp = -sqrt((2.0 * (F / B_m)));
	end
	tmp_2 = tmp;
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := If[LessEqual[F, 1.2e+67], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B$95$m), $MachinePrecision] * (-N[Sqrt[N[(B$95$m * F), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], (-N[Sqrt[N[(2.0 * N[(F / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])]

Derivation

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Alternative 20: 26.7% accurate, 5.9× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ -{\left(2 \cdot \frac{F}{B_m}\right)}^{0.5} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F) :precision binary64 (- (pow (* 2.0 (/ F B_m)) 0.5)))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	return -pow((2.0 * (F / B_m)), 0.5);
}

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 = -((2.0d0 * (f / b_m)) ** 0.5d0)
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	return -Math.pow((2.0 * (F / B_m)), 0.5);
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	return -math.pow((2.0 * (F / B_m)), 0.5)

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	return Float64(-(Float64(2.0 * Float64(F / B_m)) ^ 0.5))
end

MATLAB

B_m = abs(B);
function tmp = code(A, B_m, C, F)
	tmp = -((2.0 * (F / B_m)) ^ 0.5);
end

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := (-N[Power[N[(2.0 * N[(F / B$95$m), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision])

Derivation

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1. Add Preprocessing

Alternative 21: 26.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ -\sqrt{2 \cdot \frac{F}{B_m}} \end{array} \]

FPCore

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

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	return -sqrt((2.0 * (F / B_m)));
}

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((2.0d0 * (f / b_m)))
end function

Java

B_m = Math.abs(B);
public static double code(double A, double B_m, double C, double F) {
	return -Math.sqrt((2.0 * (F / B_m)));
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	return -math.sqrt((2.0 * (F / B_m)))

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	return Float64(-sqrt(Float64(2.0 * Float64(F / B_m))))
end

MATLAB

B_m = abs(B);
function tmp = code(A, B_m, C, F)
	tmp = -sqrt((2.0 * (F / B_m)));
end

Wolfram

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

Derivation

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Reproduce

herbie shell --seed 2023343 
(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))))