ABCF->ab-angle a

Percentage Accurate: 19.1% → 46.4%

Time: 18.4s

Alternatives: 9

Speedup: 2.0×

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: 19.1% 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: 46.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := {B_m}^{2} - \left(4 \cdot A\right) \cdot C\\ t_1 := 2 \cdot \left(t_0 \cdot F\right)\\ t_2 := -\frac{\sqrt{t_1 \cdot \left(\left(A + C\right) + \sqrt{{B_m}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_0}\\ t_3 := \frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \left(-\sqrt{A + \left(C + \mathsf{hypot}\left(A - C, B_m\right)\right)}\right)}{t_0}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(-0.5 \cdot \frac{{B_m}^{2}}{A} + 2 \cdot C\right)}}{t_0}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)} \cdot \frac{-\sqrt{2}}{B_m}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (- (pow B_m 2.0) (* (* 4.0 A) C)))
        (t_1 (* 2.0 (* t_0 F)))
        (t_2
         (-
          (/
           (sqrt
            (* t_1 (+ (+ A C) (sqrt (+ (pow B_m 2.0) (pow (- A C) 2.0))))))
           t_0)))
        (t_3
         (/
          (*
           (sqrt (* 2.0 (* F (fma B_m B_m (* A (* C -4.0))))))
           (- (sqrt (+ A (+ C (hypot (- A C) B_m))))))
          t_0)))
   (if (<= t_2 -2e-176)
     t_3
     (if (<= t_2 0.0)
       (/ (- (sqrt (* t_1 (+ (* -0.5 (/ (pow B_m 2.0) A)) (* 2.0 C))))) t_0)
       (if (<= t_2 INFINITY)
         t_3
         (* (sqrt (* F (+ A (hypot B_m A)))) (/ (- (sqrt 2.0)) B_m)))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = pow(B_m, 2.0) - ((4.0 * A) * C);
	double t_1 = 2.0 * (t_0 * F);
	double t_2 = -(sqrt((t_1 * ((A + C) + sqrt((pow(B_m, 2.0) + pow((A - C), 2.0)))))) / t_0);
	double t_3 = (sqrt((2.0 * (F * fma(B_m, B_m, (A * (C * -4.0)))))) * -sqrt((A + (C + hypot((A - C), B_m))))) / t_0;
	double tmp;
	if (t_2 <= -2e-176) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = -sqrt((t_1 * ((-0.5 * (pow(B_m, 2.0) / A)) + (2.0 * C)))) / t_0;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = sqrt((F * (A + hypot(B_m, A)))) * (-sqrt(2.0) / B_m);
	}
	return tmp;
}

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64((B_m ^ 2.0) - Float64(Float64(4.0 * A) * C))
	t_1 = Float64(2.0 * Float64(t_0 * F))
	t_2 = Float64(-Float64(sqrt(Float64(t_1 * Float64(Float64(A + C) + sqrt(Float64((B_m ^ 2.0) + (Float64(A - C) ^ 2.0)))))) / t_0))
	t_3 = 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)))))) / t_0)
	tmp = 0.0
	if (t_2 <= -2e-176)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-sqrt(Float64(t_1 * Float64(Float64(-0.5 * Float64((B_m ^ 2.0) / A)) + Float64(2.0 * C))))) / t_0);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(sqrt(Float64(F * Float64(A + hypot(B_m, A)))) * Float64(Float64(-sqrt(2.0)) / 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[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(N[Sqrt[N[(t$95$1 * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[B$95$m, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$0), $MachinePrecision])}, Block[{t$95$3 = 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] / t$95$0), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-176], t$95$3, If[LessEqual[t$95$2, 0.0], N[((-N[Sqrt[N[(t$95$1 * N[(N[(-0.5 * N[(N[Power[B$95$m, 2.0], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision] + N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[Sqrt[N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 2: 35.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := {B_m}^{2} - \left(4 \cdot A\right) \cdot C\\ t_1 := \frac{-\sqrt{2}}{B_m}\\ t_2 := 2 \cdot \left(t_0 \cdot F\right)\\ t_3 := A + \mathsf{hypot}\left(B_m, A\right)\\ \mathbf{if}\;{B_m}^{2} \leq 2 \cdot 10^{-294}:\\ \;\;\;\;\frac{-\sqrt{t_2 \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{elif}\;{B_m}^{2} \leq 10^{-34}:\\ \;\;\;\;\frac{-\sqrt{t_2 \cdot t_3}}{t_0}\\ \mathbf{elif}\;{B_m}^{2} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)} \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot t_3} \cdot t_1\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (- (pow B_m 2.0) (* (* 4.0 A) C)))
        (t_1 (/ (- (sqrt 2.0)) B_m))
        (t_2 (* 2.0 (* t_0 F)))
        (t_3 (+ A (hypot B_m A))))
   (if (<= (pow B_m 2.0) 2e-294)
     (/ (- (sqrt (* t_2 (* 2.0 C)))) t_0)
     (if (<= (pow B_m 2.0) 1e-34)
       (/ (- (sqrt (* t_2 t_3))) t_0)
       (if (<= (pow B_m 2.0) 5e+292)
         (* (sqrt (* F (+ C (hypot B_m C)))) t_1)
         (* (sqrt (* F t_3)) t_1))))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = pow(B_m, 2.0) - ((4.0 * A) * C);
	double t_1 = -sqrt(2.0) / B_m;
	double t_2 = 2.0 * (t_0 * F);
	double t_3 = A + hypot(B_m, A);
	double tmp;
	if (pow(B_m, 2.0) <= 2e-294) {
		tmp = -sqrt((t_2 * (2.0 * C))) / t_0;
	} else if (pow(B_m, 2.0) <= 1e-34) {
		tmp = -sqrt((t_2 * t_3)) / t_0;
	} else if (pow(B_m, 2.0) <= 5e+292) {
		tmp = sqrt((F * (C + hypot(B_m, C)))) * t_1;
	} else {
		tmp = sqrt((F * t_3)) * t_1;
	}
	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) - ((4.0 * A) * C);
	double t_1 = -Math.sqrt(2.0) / B_m;
	double t_2 = 2.0 * (t_0 * F);
	double t_3 = A + Math.hypot(B_m, A);
	double tmp;
	if (Math.pow(B_m, 2.0) <= 2e-294) {
		tmp = -Math.sqrt((t_2 * (2.0 * C))) / t_0;
	} else if (Math.pow(B_m, 2.0) <= 1e-34) {
		tmp = -Math.sqrt((t_2 * t_3)) / t_0;
	} else if (Math.pow(B_m, 2.0) <= 5e+292) {
		tmp = Math.sqrt((F * (C + Math.hypot(B_m, C)))) * t_1;
	} else {
		tmp = Math.sqrt((F * t_3)) * t_1;
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = math.pow(B_m, 2.0) - ((4.0 * A) * C)
	t_1 = -math.sqrt(2.0) / B_m
	t_2 = 2.0 * (t_0 * F)
	t_3 = A + math.hypot(B_m, A)
	tmp = 0
	if math.pow(B_m, 2.0) <= 2e-294:
		tmp = -math.sqrt((t_2 * (2.0 * C))) / t_0
	elif math.pow(B_m, 2.0) <= 1e-34:
		tmp = -math.sqrt((t_2 * t_3)) / t_0
	elif math.pow(B_m, 2.0) <= 5e+292:
		tmp = math.sqrt((F * (C + math.hypot(B_m, C)))) * t_1
	else:
		tmp = math.sqrt((F * t_3)) * t_1
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64((B_m ^ 2.0) - Float64(Float64(4.0 * A) * C))
	t_1 = Float64(Float64(-sqrt(2.0)) / B_m)
	t_2 = Float64(2.0 * Float64(t_0 * F))
	t_3 = Float64(A + hypot(B_m, A))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 2e-294)
		tmp = Float64(Float64(-sqrt(Float64(t_2 * Float64(2.0 * C)))) / t_0);
	elseif ((B_m ^ 2.0) <= 1e-34)
		tmp = Float64(Float64(-sqrt(Float64(t_2 * t_3))) / t_0);
	elseif ((B_m ^ 2.0) <= 5e+292)
		tmp = Float64(sqrt(Float64(F * Float64(C + hypot(B_m, C)))) * t_1);
	else
		tmp = Float64(sqrt(Float64(F * t_3)) * t_1);
	end
	return tmp
end

MATLAB

B_m = abs(B);
function tmp_2 = code(A, B_m, C, F)
	t_0 = (B_m ^ 2.0) - ((4.0 * A) * C);
	t_1 = -sqrt(2.0) / B_m;
	t_2 = 2.0 * (t_0 * F);
	t_3 = A + hypot(B_m, A);
	tmp = 0.0;
	if ((B_m ^ 2.0) <= 2e-294)
		tmp = -sqrt((t_2 * (2.0 * C))) / t_0;
	elseif ((B_m ^ 2.0) <= 1e-34)
		tmp = -sqrt((t_2 * t_3)) / t_0;
	elseif ((B_m ^ 2.0) <= 5e+292)
		tmp = sqrt((F * (C + hypot(B_m, C)))) * t_1;
	else
		tmp = sqrt((F * t_3)) * t_1;
	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[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 2e-294], N[((-N[Sqrt[N[(t$95$2 * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e-34], N[((-N[Sqrt[N[(t$95$2 * t$95$3), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 5e+292], N[(N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision], N[(N[Sqrt[N[(F * t$95$3), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 3: 35.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{-\sqrt{2}}{B_m}\\ t_1 := {B_m}^{2} - \left(4 \cdot A\right) \cdot C\\ t_2 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;{B_m}^{2} \leq 2 \cdot 10^{-294}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(t_1 \cdot F\right)\right) \cdot \left(2 \cdot C\right)}}{t_1}\\ \mathbf{elif}\;{B_m}^{2} \leq 10^{-112}:\\ \;\;\;\;-\frac{\sqrt{\left(t_2 \cdot \left(2 \cdot F\right)\right) \cdot \left(A + A\right)}}{t_2}\\ \mathbf{elif}\;{B_m}^{2} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)} \cdot t_0\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (- (sqrt 2.0)) B_m))
        (t_1 (- (pow B_m 2.0) (* (* 4.0 A) C)))
        (t_2 (fma B_m B_m (* A (* C -4.0)))))
   (if (<= (pow B_m 2.0) 2e-294)
     (/ (- (sqrt (* (* 2.0 (* t_1 F)) (* 2.0 C)))) t_1)
     (if (<= (pow B_m 2.0) 1e-112)
       (- (/ (sqrt (* (* t_2 (* 2.0 F)) (+ A A))) t_2))
       (if (<= (pow B_m 2.0) 5e+292)
         (* (sqrt (* F (+ C (hypot B_m C)))) t_0)
         (* (sqrt (* F (+ A (hypot B_m A)))) 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 t_1 = pow(B_m, 2.0) - ((4.0 * A) * C);
	double t_2 = fma(B_m, B_m, (A * (C * -4.0)));
	double tmp;
	if (pow(B_m, 2.0) <= 2e-294) {
		tmp = -sqrt(((2.0 * (t_1 * F)) * (2.0 * C))) / t_1;
	} else if (pow(B_m, 2.0) <= 1e-112) {
		tmp = -(sqrt(((t_2 * (2.0 * F)) * (A + A))) / t_2);
	} else if (pow(B_m, 2.0) <= 5e+292) {
		tmp = sqrt((F * (C + hypot(B_m, C)))) * t_0;
	} else {
		tmp = sqrt((F * (A + hypot(B_m, A)))) * 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)
	t_1 = Float64((B_m ^ 2.0) - Float64(Float64(4.0 * A) * C))
	t_2 = fma(B_m, B_m, Float64(A * Float64(C * -4.0)))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 2e-294)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_1 * F)) * Float64(2.0 * C)))) / t_1);
	elseif ((B_m ^ 2.0) <= 1e-112)
		tmp = Float64(-Float64(sqrt(Float64(Float64(t_2 * Float64(2.0 * F)) * Float64(A + A))) / t_2));
	elseif ((B_m ^ 2.0) <= 5e+292)
		tmp = Float64(sqrt(Float64(F * Float64(C + hypot(B_m, C)))) * t_0);
	else
		tmp = Float64(sqrt(Float64(F * Float64(A + hypot(B_m, A)))) * 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[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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], 2e-294], N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$1 * F), $MachinePrecision]), $MachinePrecision] * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision], If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 1e-112], (-N[(N[Sqrt[N[(N[(t$95$2 * N[(2.0 * F), $MachinePrecision]), $MachinePrecision] * N[(A + A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$2), $MachinePrecision]), If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 5e+292], N[(N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], N[(N[Sqrt[N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]]]]]]]

Derivation

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

Alternative 4: 36.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, -4 \cdot \left(A \cdot C\right)\right)\\ t_1 := {B_m}^{2} - \left(4 \cdot A\right) \cdot C\\ \mathbf{if}\;B_m \leq 6.8 \cdot 10^{-143}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(t_1 \cdot F\right)\right) \cdot \left(2 \cdot C\right)}}{t_1}\\ \mathbf{elif}\;B_m \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B_m\right)\right) \cdot t_0\right) \cdot \left(2 \cdot F\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)} \cdot \frac{-\sqrt{2}}{B_m}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (fma B_m B_m (* -4.0 (* A C))))
        (t_1 (- (pow B_m 2.0) (* (* 4.0 A) C))))
   (if (<= B_m 6.8e-143)
     (/ (- (sqrt (* (* 2.0 (* t_1 F)) (* 2.0 C)))) t_1)
     (if (<= B_m 1.15e-16)
       (/ (- (sqrt (* (* (+ (+ A C) (hypot (- A C) B_m)) t_0) (* 2.0 F)))) t_0)
       (* (sqrt (* F (+ A (hypot B_m A)))) (/ (- (sqrt 2.0)) 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 t_1 = pow(B_m, 2.0) - ((4.0 * A) * C);
	double tmp;
	if (B_m <= 6.8e-143) {
		tmp = -sqrt(((2.0 * (t_1 * F)) * (2.0 * C))) / t_1;
	} else if (B_m <= 1.15e-16) {
		tmp = -sqrt(((((A + C) + hypot((A - C), B_m)) * t_0) * (2.0 * F))) / t_0;
	} else {
		tmp = sqrt((F * (A + hypot(B_m, A)))) * (-sqrt(2.0) / 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)))
	t_1 = Float64((B_m ^ 2.0) - Float64(Float64(4.0 * A) * C))
	tmp = 0.0
	if (B_m <= 6.8e-143)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_1 * F)) * Float64(2.0 * C)))) / t_1);
	elseif (B_m <= 1.15e-16)
		tmp = Float64(Float64(-sqrt(Float64(Float64(Float64(Float64(A + C) + hypot(Float64(A - C), B_m)) * t_0) * Float64(2.0 * F)))) / t_0);
	else
		tmp = Float64(sqrt(Float64(F * Float64(A + hypot(B_m, A)))) * Float64(Float64(-sqrt(2.0)) / 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]}, Block[{t$95$1 = N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B$95$m, 6.8e-143], N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$1 * F), $MachinePrecision]), $MachinePrecision] * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision], If[LessEqual[B$95$m, 1.15e-16], N[((-N[Sqrt[N[(N[(N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] * N[(2.0 * F), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], N[(N[Sqrt[N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 38.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \mathsf{fma}\left(B_m, B_m, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := {B_m}^{2} - \left(4 \cdot A\right) \cdot C\\ \mathbf{if}\;B_m \leq 1.55 \cdot 10^{-143}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(t_1 \cdot F\right)\right) \cdot \left(2 \cdot C\right)}}{t_1}\\ \mathbf{elif}\;B_m \leq 6.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{-\sqrt{\left(t_0 \cdot \left(2 \cdot F\right)\right) \cdot \left(A + \left(C + \mathsf{hypot}\left(B_m, A - C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)} \cdot \frac{-\sqrt{2}}{B_m}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (fma B_m B_m (* A (* C -4.0))))
        (t_1 (- (pow B_m 2.0) (* (* 4.0 A) C))))
   (if (<= B_m 1.55e-143)
     (/ (- (sqrt (* (* 2.0 (* t_1 F)) (* 2.0 C)))) t_1)
     (if (<= B_m 6.8e+14)
       (/ (- (sqrt (* (* t_0 (* 2.0 F)) (+ A (+ C (hypot B_m (- A C))))))) t_0)
       (* (sqrt (* F (+ A (hypot B_m A)))) (/ (- (sqrt 2.0)) 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 t_1 = pow(B_m, 2.0) - ((4.0 * A) * C);
	double tmp;
	if (B_m <= 1.55e-143) {
		tmp = -sqrt(((2.0 * (t_1 * F)) * (2.0 * C))) / t_1;
	} else if (B_m <= 6.8e+14) {
		tmp = -sqrt(((t_0 * (2.0 * F)) * (A + (C + hypot(B_m, (A - C)))))) / t_0;
	} else {
		tmp = sqrt((F * (A + hypot(B_m, A)))) * (-sqrt(2.0) / 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)))
	t_1 = Float64((B_m ^ 2.0) - Float64(Float64(4.0 * A) * C))
	tmp = 0.0
	if (B_m <= 1.55e-143)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_1 * F)) * Float64(2.0 * C)))) / t_1);
	elseif (B_m <= 6.8e+14)
		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(sqrt(Float64(F * Float64(A + hypot(B_m, A)))) * Float64(Float64(-sqrt(2.0)) / 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]}, Block[{t$95$1 = N[(N[Power[B$95$m, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B$95$m, 1.55e-143], N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$1 * F), $MachinePrecision]), $MachinePrecision] * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision], If[LessEqual[B$95$m, 6.8e+14], 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[Sqrt[N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 33.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := {B_m}^{2} - \left(4 \cdot A\right) \cdot C\\ \mathbf{if}\;{B_m}^{2} \leq 2 \cdot 10^{-290}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(t_0 \cdot F\right)\right) \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)} \cdot \frac{-\sqrt{2}}{B_m}\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (- (pow B_m 2.0) (* (* 4.0 A) C))))
   (if (<= (pow B_m 2.0) 2e-290)
     (/ (- (sqrt (* (* 2.0 (* t_0 F)) (* 2.0 C)))) t_0)
     (* (sqrt (* F (+ A (hypot B_m A)))) (/ (- (sqrt 2.0)) B_m)))))

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	double t_0 = pow(B_m, 2.0) - ((4.0 * A) * C);
	double tmp;
	if (pow(B_m, 2.0) <= 2e-290) {
		tmp = -sqrt(((2.0 * (t_0 * F)) * (2.0 * C))) / t_0;
	} else {
		tmp = sqrt((F * (A + hypot(B_m, A)))) * (-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 t_0 = Math.pow(B_m, 2.0) - ((4.0 * A) * C);
	double tmp;
	if (Math.pow(B_m, 2.0) <= 2e-290) {
		tmp = -Math.sqrt(((2.0 * (t_0 * F)) * (2.0 * C))) / t_0;
	} else {
		tmp = Math.sqrt((F * (A + Math.hypot(B_m, A)))) * (-Math.sqrt(2.0) / B_m);
	}
	return tmp;
}

Python

B_m = math.fabs(B)
def code(A, B_m, C, F):
	t_0 = math.pow(B_m, 2.0) - ((4.0 * A) * C)
	tmp = 0
	if math.pow(B_m, 2.0) <= 2e-290:
		tmp = -math.sqrt(((2.0 * (t_0 * F)) * (2.0 * C))) / t_0
	else:
		tmp = math.sqrt((F * (A + math.hypot(B_m, A)))) * (-math.sqrt(2.0) / B_m)
	return tmp

Julia

B_m = abs(B)
function code(A, B_m, C, F)
	t_0 = Float64((B_m ^ 2.0) - Float64(Float64(4.0 * A) * C))
	tmp = 0.0
	if ((B_m ^ 2.0) <= 2e-290)
		tmp = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_0 * F)) * Float64(2.0 * C)))) / t_0);
	else
		tmp = Float64(sqrt(Float64(F * Float64(A + hypot(B_m, A)))) * 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)
	t_0 = (B_m ^ 2.0) - ((4.0 * A) * C);
	tmp = 0.0;
	if ((B_m ^ 2.0) <= 2e-290)
		tmp = -sqrt(((2.0 * (t_0 * F)) * (2.0 * C))) / t_0;
	else
		tmp = sqrt((F * (A + hypot(B_m, A)))) * (-sqrt(2.0) / 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[Power[B$95$m, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Power[B$95$m, 2.0], $MachinePrecision], 2e-290], N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision] * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], N[(N[Sqrt[N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 7: 31.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \begin{array}{l} t_0 := \frac{-\sqrt{2}}{B_m}\\ \mathbf{if}\;A \leq 10^{-127}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B_m, A\right)\right)} \cdot t_0\\ \end{array} \end{array} \]

FPCore

B_m = (fabs.f64 B)
(FPCore (A B_m C F)
 :precision binary64
 (let* ((t_0 (/ (- (sqrt 2.0)) B_m)))
   (if (<= A 1e-127)
     (* (sqrt (* F (+ C (hypot B_m C)))) t_0)
     (* (sqrt (* F (+ A (hypot B_m A)))) 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 (A <= 1e-127) {
		tmp = sqrt((F * (C + hypot(B_m, C)))) * t_0;
	} else {
		tmp = sqrt((F * (A + hypot(B_m, A)))) * 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 (A <= 1e-127) {
		tmp = Math.sqrt((F * (C + Math.hypot(B_m, C)))) * t_0;
	} else {
		tmp = Math.sqrt((F * (A + Math.hypot(B_m, A)))) * 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 A <= 1e-127:
		tmp = math.sqrt((F * (C + math.hypot(B_m, C)))) * t_0
	else:
		tmp = math.sqrt((F * (A + math.hypot(B_m, A)))) * 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 (A <= 1e-127)
		tmp = Float64(sqrt(Float64(F * Float64(C + hypot(B_m, C)))) * t_0);
	else
		tmp = Float64(sqrt(Float64(F * Float64(A + hypot(B_m, A)))) * 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 (A <= 1e-127)
		tmp = sqrt((F * (C + hypot(B_m, C)))) * t_0;
	else
		tmp = sqrt((F * (A + hypot(B_m, A)))) * 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[A, 1e-127], N[(N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], N[(N[Sqrt[N[(F * N[(A + N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]]]

Derivation

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

Alternative 8: 29.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} B_m = \left|B\right| \\ \sqrt{F \cdot \left(C + \mathsf{hypot}\left(B_m, C\right)\right)} \cdot \frac{-\sqrt{2}}{B_m} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

B_m = N[Abs[B], $MachinePrecision]
code[A_, B$95$m_, C_, F_] := N[(N[Sqrt[N[(F * N[(C + N[Sqrt[B$95$m ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 9: 0.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

B_m = fabs(B);
double code(double A, double B_m, double C, double F) {
	return sqrt((F / C)) * (sqrt(2.0) * -sqrt(-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 = sqrt((f / c)) * (sqrt(2.0d0) * -sqrt((-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.sqrt((F / C)) * (Math.sqrt(2.0) * -Math.sqrt(-0.5));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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))))