ABCF->ab-angle b

Average Accuracy: 17.6% → 33.6%

Time: 1.0min

Precision: binary64

Cost: 27664

Math

\[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

↓

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := \sqrt{-\frac{F}{A}}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-63}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-16, C \cdot \left(C \cdot \left(F \cdot A\right)\right), 2 \cdot \left(\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right) \cdot \left(C + \frac{C}{\frac{A - C}{A}}\right)\right)\right)} \cdot \frac{1}{-t_1}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-107}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{F \cdot \left(C + C\right)} \cdot \frac{-\sqrt{2 \cdot t_1}}{t_1}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-292}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

FPCore

(FPCore (A B C F)
 :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))))

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (- (* B B) (* 4.0 (* C A))))
        (t_1 (fma B B (* A (* C -4.0))))
        (t_2 (sqrt (- (/ F A)))))
   (if (<= B -4.5e+35)
     (/ (sqrt (* F (- C (hypot B C)))) (/ B (sqrt 2.0)))
     (if (<= B -1.45e-63)
       (*
        (sqrt
         (fma
          -16.0
          (* C (* C (* F A)))
          (* 2.0 (* (* 2.0 (* F (* B B))) (+ C (/ C (/ (- A C) A)))))))
        (/ 1.0 (- t_1)))
       (if (<= B -4.3e-107)
         (/
          (-
           (sqrt
            (*
             2.0
             (* (* F t_0) (+ A (- C (sqrt (+ (* B B) (pow (- A C) 2.0)))))))))
          t_0)
         (if (<= B -9e-240)
           (* (sqrt (* F (+ C C))) (/ (- (sqrt (* 2.0 t_1))) t_1))
           (if (<= B -1.1e-292)
             (* (sqrt (* F (* (* A -8.0) (* C (+ A A))))) (/ -1.0 t_1))
             (if (<= B 1.15e-263)
               t_2
               (if (<= B 2.8e-191)
                 (/ (- (sqrt (* (* A -8.0) (* (+ A A) (* F C))))) t_1)
                 (if (<= B 1.55e-44)
                   t_2
                   (*
                    (sqrt (* F (- (+ C A) (hypot B (- A C)))))
                    (/ (- (sqrt 2.0)) B))))))))))))

C

double code(double A, double B, double C, double F) {
	return -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));
}

↓

double code(double A, double B, double C, double F) {
	double t_0 = (B * B) - (4.0 * (C * A));
	double t_1 = fma(B, B, (A * (C * -4.0)));
	double t_2 = sqrt(-(F / A));
	double tmp;
	if (B <= -4.5e+35) {
		tmp = sqrt((F * (C - hypot(B, C)))) / (B / sqrt(2.0));
	} else if (B <= -1.45e-63) {
		tmp = sqrt(fma(-16.0, (C * (C * (F * A))), (2.0 * ((2.0 * (F * (B * B))) * (C + (C / ((A - C) / A))))))) * (1.0 / -t_1);
	} else if (B <= -4.3e-107) {
		tmp = -sqrt((2.0 * ((F * t_0) * (A + (C - sqrt(((B * B) + pow((A - C), 2.0)))))))) / t_0;
	} else if (B <= -9e-240) {
		tmp = sqrt((F * (C + C))) * (-sqrt((2.0 * t_1)) / t_1);
	} else if (B <= -1.1e-292) {
		tmp = sqrt((F * ((A * -8.0) * (C * (A + A))))) * (-1.0 / t_1);
	} else if (B <= 1.15e-263) {
		tmp = t_2;
	} else if (B <= 2.8e-191) {
		tmp = -sqrt(((A * -8.0) * ((A + A) * (F * C)))) / t_1;
	} else if (B <= 1.55e-44) {
		tmp = t_2;
	} else {
		tmp = sqrt((F * ((C + A) - hypot(B, (A - C))))) * (-sqrt(2.0) / B);
	}
	return tmp;
}

Julia

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

↓

function code(A, B, C, F)
	t_0 = Float64(Float64(B * B) - Float64(4.0 * Float64(C * A)))
	t_1 = fma(B, B, Float64(A * Float64(C * -4.0)))
	t_2 = sqrt(Float64(-Float64(F / A)))
	tmp = 0.0
	if (B <= -4.5e+35)
		tmp = Float64(sqrt(Float64(F * Float64(C - hypot(B, C)))) / Float64(B / sqrt(2.0)));
	elseif (B <= -1.45e-63)
		tmp = Float64(sqrt(fma(-16.0, Float64(C * Float64(C * Float64(F * A))), Float64(2.0 * Float64(Float64(2.0 * Float64(F * Float64(B * B))) * Float64(C + Float64(C / Float64(Float64(A - C) / A))))))) * Float64(1.0 / Float64(-t_1)));
	elseif (B <= -4.3e-107)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(Float64(F * t_0) * Float64(A + Float64(C - sqrt(Float64(Float64(B * B) + (Float64(A - C) ^ 2.0))))))))) / t_0);
	elseif (B <= -9e-240)
		tmp = Float64(sqrt(Float64(F * Float64(C + C))) * Float64(Float64(-sqrt(Float64(2.0 * t_1))) / t_1));
	elseif (B <= -1.1e-292)
		tmp = Float64(sqrt(Float64(F * Float64(Float64(A * -8.0) * Float64(C * Float64(A + A))))) * Float64(-1.0 / t_1));
	elseif (B <= 1.15e-263)
		tmp = t_2;
	elseif (B <= 2.8e-191)
		tmp = Float64(Float64(-sqrt(Float64(Float64(A * -8.0) * Float64(Float64(A + A) * Float64(F * C))))) / t_1);
	elseif (B <= 1.55e-44)
		tmp = t_2;
	else
		tmp = Float64(sqrt(Float64(F * Float64(Float64(C + A) - hypot(B, Float64(A - C))))) * Float64(Float64(-sqrt(2.0)) / B));
	end
	return tmp
end

Wolfram

code[A_, B_, C_, F_] := N[((-N[Sqrt[N[(N[(2.0 * N[(N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision] * 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]) / N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(N[(B * B), $MachinePrecision] - N[(4.0 * N[(C * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(B * B + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[(-N[(F / A), $MachinePrecision])], $MachinePrecision]}, If[LessEqual[B, -4.5e+35], N[(N[Sqrt[N[(F * N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(B / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.45e-63], N[(N[Sqrt[N[(-16.0 * N[(C * N[(C * N[(F * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(N[(2.0 * N[(F * N[(B * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(C + N[(C / N[(N[(A - C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(1.0 / (-t$95$1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.3e-107], N[((-N[Sqrt[N[(2.0 * N[(N[(F * t$95$0), $MachinePrecision] * N[(A + N[(C - N[Sqrt[N[(N[(B * B), $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[B, -9e-240], N[(N[Sqrt[N[(F * N[(C + C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.1e-292], N[(N[Sqrt[N[(F * N[(N[(A * -8.0), $MachinePrecision] * N[(C * N[(A + A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e-263], t$95$2, If[LessEqual[B, 2.8e-191], N[((-N[Sqrt[N[(N[(A * -8.0), $MachinePrecision] * N[(N[(A + A), $MachinePrecision] * N[(F * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision], If[LessEqual[B, 1.55e-44], t$95$2, N[(N[Sqrt[N[(F * N[(N[(C + A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -4.4999999999999997e35

   1. Initial program 11.5%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 13.5%

      \[\leadsto \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof

      [Start] 11.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 1.1%

      \[\leadsto \color{blue}{\sqrt{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)\right)}{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}}} \]

   4. Simplified 1.4%

      \[\leadsto \color{blue}{\sqrt{\frac{\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)}{\frac{{\left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}}} \]
      Proof

      [Start] 1.1	\[ \sqrt{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)\right)}{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}} \]
      associate-/l* [=>] 1.4	\[ \sqrt{\color{blue}{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}}} \]
      associate-*r* [=>] 1.4	\[ \sqrt{\frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)}{\frac{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}} \]
      associate-*r* [=>] 1.4	\[ \sqrt{\frac{\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)}{\frac{{\left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}} \]

   5. Taylor expanded in A around 0 17.7%

      \[\leadsto \color{blue}{\sqrt{\left(C - \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \cdot \frac{\sqrt{2}}{B}} \]

   6. Simplified 17.7%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(C - \sqrt{B \cdot B + C \cdot C}\right)} \cdot \frac{\sqrt{2}}{B}} \]
      Proof

      [Start] 17.7	\[ \sqrt{\left(C - \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \cdot \frac{\sqrt{2}}{B} \]
      *-commutative [=>] 17.7	\[ \sqrt{\color{blue}{F \cdot \left(C - \sqrt{{B}^{2} + {C}^{2}}\right)}} \cdot \frac{\sqrt{2}}{B} \]
      unpow2 [=>] 17.7	\[ \sqrt{F \cdot \left(C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}\right)} \cdot \frac{\sqrt{2}}{B} \]
      unpow2 [=>] 17.7	\[ \sqrt{F \cdot \left(C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}\right)} \cdot \frac{\sqrt{2}}{B} \]

   7. Applied egg-rr 48.2%

      \[\leadsto \color{blue}{\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}} \]

   if -4.4999999999999997e35 < B < -1.44999999999999987e-63

   1. Initial program 34.6%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 43.8%

      \[\leadsto \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof

      [Start] 34.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in B around 0 10.4%

      \[\leadsto \frac{-\sqrt{\color{blue}{-16 \cdot \left(A \cdot \left({C}^{2} \cdot F\right)\right) + 2 \cdot \left(F \cdot \left(\left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right) \cdot {B}^{2}\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   4. Simplified 10.4%

      \[\leadsto \frac{-\sqrt{\color{blue}{\mathsf{fma}\left(-16, A \cdot \left(F \cdot \left(C \cdot C\right)\right), \left(2 \cdot F\right) \cdot \left(\left(B \cdot B\right) \cdot \left(2 \cdot \left(\frac{A \cdot C}{A - C} + C\right)\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof

      [Start] 10.4	\[ \frac{-\sqrt{-16 \cdot \left(A \cdot \left({C}^{2} \cdot F\right)\right) + 2 \cdot \left(F \cdot \left(\left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right) \cdot {B}^{2}\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      fma-def [=>] 10.4	\[ \frac{-\sqrt{\color{blue}{\mathsf{fma}\left(-16, A \cdot \left({C}^{2} \cdot F\right), 2 \cdot \left(F \cdot \left(\left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right) \cdot {B}^{2}\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      *-commutative [=>] 10.4	\[ \frac{-\sqrt{\mathsf{fma}\left(-16, A \cdot \color{blue}{\left(F \cdot {C}^{2}\right)}, 2 \cdot \left(F \cdot \left(\left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right) \cdot {B}^{2}\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      unpow2 [=>] 10.4	\[ \frac{-\sqrt{\mathsf{fma}\left(-16, A \cdot \left(F \cdot \color{blue}{\left(C \cdot C\right)}\right), 2 \cdot \left(F \cdot \left(\left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right) \cdot {B}^{2}\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 10.4	\[ \frac{-\sqrt{\mathsf{fma}\left(-16, A \cdot \left(F \cdot \left(C \cdot C\right)\right), \color{blue}{\left(2 \cdot F\right) \cdot \left(\left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right) \cdot {B}^{2}\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      *-commutative [=>] 10.4	\[ \frac{-\sqrt{\mathsf{fma}\left(-16, A \cdot \left(F \cdot \left(C \cdot C\right)\right), \left(2 \cdot F\right) \cdot \color{blue}{\left({B}^{2} \cdot \left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right)\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      unpow2 [=>] 10.4	\[ \frac{-\sqrt{\mathsf{fma}\left(-16, A \cdot \left(F \cdot \left(C \cdot C\right)\right), \left(2 \cdot F\right) \cdot \left(\color{blue}{\left(B \cdot B\right)} \cdot \left(2 \cdot \frac{A \cdot C}{A - C} + 2 \cdot C\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      distribute-lft-out [=>] 10.4	\[ \frac{-\sqrt{\mathsf{fma}\left(-16, A \cdot \left(F \cdot \left(C \cdot C\right)\right), \left(2 \cdot F\right) \cdot \left(\left(B \cdot B\right) \cdot \color{blue}{\left(2 \cdot \left(\frac{A \cdot C}{A - C} + C\right)\right)}\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   5. Applied egg-rr 14.1%

      \[\leadsto \color{blue}{\sqrt{\mathsf{fma}\left(-16, \left(\left(A \cdot F\right) \cdot C\right) \cdot C, 2 \cdot \left(\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right) \cdot \left(C + \frac{C}{\frac{A - C}{A}}\right)\right)\right)} \cdot \frac{1}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   if -1.44999999999999987e-63 < B < -4.2999999999999997e-107

   1. Initial program 25.2%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 26.1%

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      Proof

      [Start] 25.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   if -4.2999999999999997e-107 < B < -9.0000000000000003e-240

   1. Initial program 18.0%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 27.1%

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(C - \left(\mathsf{hypot}\left(B, A - C\right) - A\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}} \]
      Proof

      [Start] 18.0	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 20.9%

      \[\leadsto \frac{-\color{blue}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   4. Simplified 20.9%

      \[\leadsto \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      Proof

      [Start] 20.9	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 20.9	\[ \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 20.9	\[ \frac{-\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \color{blue}{\left(C \cdot -4\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   5. Applied egg-rr 19.1%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]

   6. Simplified 19.7%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      Proof

      [Start] 19.1	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-lft-neg-out [=>] 19.1	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      associate-*r/ [=>] 19.7	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\color{blue}{\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}\right) \]
      *-rgt-identity [=>] 19.7	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\color{blue}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]

   7. Taylor expanded in A around inf 14.9%

      \[\leadsto \color{blue}{\sqrt{\left(C - -1 \cdot C\right) \cdot F}} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]

   8. Simplified 14.9%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(C + C\right)}} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      Proof

      [Start] 14.9	\[ \sqrt{\left(C - -1 \cdot C\right) \cdot F} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      *-commutative [=>] 14.9	\[ \sqrt{\color{blue}{F \cdot \left(C - -1 \cdot C\right)}} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      sub-neg [=>] 14.9	\[ \sqrt{F \cdot \color{blue}{\left(C + \left(--1 \cdot C\right)\right)}} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      mul-1-neg [=>] 14.9	\[ \sqrt{F \cdot \left(C + \left(-\color{blue}{\left(-C\right)}\right)\right)} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      remove-double-neg [=>] 14.9	\[ \sqrt{F \cdot \left(C + \color{blue}{C}\right)} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]

   if -9.0000000000000003e-240 < B < -1.10000000000000006e-292

   1. Initial program 13.6%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 26.1%

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(C - \left(\mathsf{hypot}\left(B, A - C\right) - A\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}} \]
      Proof

      [Start] 13.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 15.6%

      \[\leadsto \frac{-\color{blue}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   4. Simplified 15.6%

      \[\leadsto \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      Proof

      [Start] 15.6	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 15.6	\[ \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 15.6	\[ \frac{-\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \color{blue}{\left(C \cdot -4\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   5. Applied egg-rr 21.9%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)\right)} \cdot \frac{1}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   6. Simplified 23.3%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(\left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot 2\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof

      [Start] 21.9	\[ \sqrt{F \cdot \left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)\right)} \cdot \frac{1}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 21.9	\[ \sqrt{F \cdot \color{blue}{\left(\left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot 2\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}} \cdot \frac{1}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate--l+ [=>] 23.3	\[ \sqrt{F \cdot \left(\left(\color{blue}{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot 2\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \frac{1}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      neg-mul-1 [=>] 23.3	\[ \sqrt{F \cdot \left(\left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot 2\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \frac{1}{\color{blue}{-1 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      associate-/r* [=>] 23.3	\[ \sqrt{F \cdot \left(\left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot 2\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \color{blue}{\frac{\frac{1}{-1}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      metadata-eval [=>] 23.3	\[ \sqrt{F \cdot \left(\left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot 2\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \frac{\color{blue}{-1}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   7. Taylor expanded in C around inf 19.0%

      \[\leadsto \sqrt{F \cdot \color{blue}{\left(-8 \cdot \left(A \cdot \left(\left(A - -1 \cdot A\right) \cdot C\right)\right)\right)}} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   8. Simplified 19.0%

      \[\leadsto \sqrt{F \cdot \color{blue}{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot \left(A - \left(-A\right)\right)\right)\right)}} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof

      [Start] 19.0	\[ \sqrt{F \cdot \left(-8 \cdot \left(A \cdot \left(\left(A - -1 \cdot A\right) \cdot C\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 19.0	\[ \sqrt{F \cdot \color{blue}{\left(\left(-8 \cdot A\right) \cdot \left(\left(A - -1 \cdot A\right) \cdot C\right)\right)}} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      *-commutative [=>] 19.0	\[ \sqrt{F \cdot \left(\left(-8 \cdot A\right) \cdot \color{blue}{\left(C \cdot \left(A - -1 \cdot A\right)\right)}\right)} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      mul-1-neg [=>] 19.0	\[ \sqrt{F \cdot \left(\left(-8 \cdot A\right) \cdot \left(C \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   if -1.10000000000000006e-292 < B < 1.15000000000000001e-263 or 2.80000000000000012e-191 < B < 1.54999999999999992e-44

   1. Initial program 20.9%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 28.9%

      \[\leadsto \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof

      [Start] 20.9	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 8.3%

      \[\leadsto \color{blue}{\sqrt{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)\right)}{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}}} \]

   4. Simplified 8.7%

      \[\leadsto \color{blue}{\sqrt{\frac{\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)}{\frac{{\left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}}} \]
      Proof

      [Start] 8.3	\[ \sqrt{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)\right)}{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}} \]
      associate-/l* [=>] 8.7	\[ \sqrt{\color{blue}{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}}} \]
      associate-*r* [=>] 8.7	\[ \sqrt{\frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)}{\frac{{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}} \]
      associate-*r* [=>] 8.7	\[ \sqrt{\frac{\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)}{\frac{{\left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)\right)}^{2}}{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}} \]

   5. Taylor expanded in B around 0 19.3%

      \[\leadsto \sqrt{\color{blue}{-1 \cdot \frac{F}{A}}} \]

   6. Simplified 19.3%

      \[\leadsto \sqrt{\color{blue}{-\frac{F}{A}}} \]
      Proof

      [Start] 19.3	\[ \sqrt{-1 \cdot \frac{F}{A}} \]
      mul-1-neg [=>] 19.3	\[ \sqrt{\color{blue}{-\frac{F}{A}}} \]

   if 1.15000000000000001e-263 < B < 2.80000000000000012e-191

   1. Initial program 14.5%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 24.9%

      \[\leadsto \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof

      [Start] 14.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in C around inf 17.7%

      \[\leadsto \frac{-\sqrt{\color{blue}{-8 \cdot \left(A \cdot \left(\left(A - -1 \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   4. Simplified 17.7%

      \[\leadsto \frac{-\sqrt{\color{blue}{\left(-8 \cdot A\right) \cdot \left(\left(F \cdot C\right) \cdot \left(A - \left(-A\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof

      [Start] 17.7	\[ \frac{-\sqrt{-8 \cdot \left(A \cdot \left(\left(A - -1 \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 17.7	\[ \frac{-\sqrt{\color{blue}{\left(-8 \cdot A\right) \cdot \left(\left(A - -1 \cdot A\right) \cdot \left(C \cdot F\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      *-commutative [=>] 17.7	\[ \frac{-\sqrt{\left(-8 \cdot A\right) \cdot \color{blue}{\left(\left(C \cdot F\right) \cdot \left(A - -1 \cdot A\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      *-commutative [=>] 17.7	\[ \frac{-\sqrt{\left(-8 \cdot A\right) \cdot \left(\color{blue}{\left(F \cdot C\right)} \cdot \left(A - -1 \cdot A\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      mul-1-neg [=>] 17.7	\[ \frac{-\sqrt{\left(-8 \cdot A\right) \cdot \left(\left(F \cdot C\right) \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   if 1.54999999999999992e-44 < B

   1. Initial program 16.1%

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   2. Simplified 20.0%

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(C - \left(\mathsf{hypot}\left(B, A - C\right) - A\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}} \]
      Proof

      [Start] 16.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 26.0%

      \[\leadsto \frac{-\color{blue}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   4. Simplified 26.0%

      \[\leadsto \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      Proof

      [Start] 26.0	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 26.0	\[ \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 26.0	\[ \frac{-\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \color{blue}{\left(C \cdot -4\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   5. Applied egg-rr 25.8%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]

   6. Simplified 25.8%

      \[\leadsto \color{blue}{\sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      Proof

      [Start] 25.8	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-lft-neg-out [=>] 25.8	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      associate-*r/ [=>] 25.8	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\color{blue}{\frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}\right) \]
      *-rgt-identity [=>] 25.8	\[ \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\color{blue}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]

   7. Taylor expanded in B around inf 48.1%

      \[\leadsto \sqrt{F \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\color{blue}{\frac{\sqrt{2}}{B}}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-63}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-16, C \cdot \left(C \cdot \left(F \cdot A\right)\right), 2 \cdot \left(\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right) \cdot \left(C + \frac{C}{\frac{A - C}{A}}\right)\right)\right)} \cdot \frac{1}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-107}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B - 4 \cdot \left(C \cdot A\right)\right)\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{F \cdot \left(C + C\right)} \cdot \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-292}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-263}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-44}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	38.5%
Cost	60048

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;B \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C + \left(A - t_1\right)\right)\right) \cdot t_0\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-61}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+123}:\\ \;\;\;\;\frac{\sqrt{F \cdot \mathsf{fma}\left({\left(\sqrt[3]{A}\right)}^{2}, \sqrt[3]{A}, C - t_1\right)} \cdot \left(-\sqrt{2 \cdot t_0}\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - t_1\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 2
Accuracy	38.5%
Cost	34384

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;B \leq -2.85 \cdot 10^{+38}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C + \left(A - t_1\right)\right)\right) \cdot t_0\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-61}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+123}:\\ \;\;\;\;\frac{\sqrt{2 \cdot t_0} \cdot \left(-\sqrt{F \cdot \left(A + \left(C - t_1\right)\right)}\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - t_1\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 3
Accuracy	38.2%
Cost	27984

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C + \left(A - t_1\right)\right)\right) \cdot t_0\right)}}{t_0}\\ \mathbf{if}\;B \leq -8.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - t_1\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 4
Accuracy	38.1%
Cost	27984

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;B \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-294}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C + \left(A - t_1\right)\right)\right) \cdot t_0\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;\frac{-\sqrt{t_0 \cdot \left(\left(A + \left(C - t_1\right)\right) \cdot \left(F \cdot 2\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - t_1\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 5
Accuracy	34.7%
Cost	21964

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{A}}\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(F \cdot 2\right) \cdot \left(C \cdot 2\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_2\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-252}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -4.7 \cdot 10^{-297}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 6
Accuracy	34.5%
Cost	21964

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := \sqrt{-\frac{F}{A}}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -2.35 \cdot 10^{-63}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-16, C \cdot \left(C \cdot \left(F \cdot A\right)\right), 2 \cdot \left(\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right) \cdot \left(C + \frac{C}{\frac{A - C}{A}}\right)\right)\right)} \cdot \frac{1}{-t_1}\\ \mathbf{elif}\;B \leq -1.75 \cdot 10^{-105}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-249}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-294}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.72 \cdot 10^{-192}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 7
Accuracy	34.1%
Cost	21216

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{A}}\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\sqrt{t_2}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(F \cdot 2\right) \cdot \left(C \cdot 2\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -4.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{\sqrt{t_2 \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-252}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-297}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-192}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 8
Accuracy	35.3%
Cost	20952

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{A}}\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.85 \cdot 10^{-127}:\\ \;\;\;\;\frac{\sqrt{\left(F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-255}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-296}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 9
Accuracy	24.8%
Cost	14740

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{A}}\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -1.6 \cdot 10^{-128}:\\ \;\;\;\;\frac{\sqrt{\left(F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-257}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-305}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-258}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_1\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 10
Accuracy	25.4%
Cost	14740

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{A}}\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := \frac{-1}{t_1}\\ t_3 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{\left(F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -1.22 \cdot 10^{-250}:\\ \;\;\;\;t_2 \cdot \sqrt{-8 \cdot \left(\left(F \cdot C\right) \cdot \left(A \cdot \left(C + C\right)\right)\right)}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot t_2\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_3\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 11
Accuracy	25.5%
Cost	14740

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{A}}\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -4.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{\sqrt{\left(F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-255}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(A \cdot -8\right) \cdot \left(C \cdot \left(A + A\right)\right)\right)} \cdot \frac{-1}{t_2}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(A + A\right) \cdot \left(F \cdot C\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_1\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 12
Accuracy	25.7%
Cost	14408

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -1.36 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{\left(F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-278}:\\ \;\;\;\;\frac{-1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot \sqrt{-8 \cdot \left(\left(F \cdot C\right) \cdot \left(A \cdot \left(C + C\right)\right)\right)}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{+119}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 13
Accuracy	22.1%
Cost	13772

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{C}}\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_2 := \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(B + C\right)}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -8.4 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.4 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-262}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+120}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_1\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 14
Accuracy	24.6%
Cost	13572

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;\frac{\sqrt{\left(F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot 2}}{B}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-256}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-193}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 15
Accuracy	19.1%
Cost	13452

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -4.2 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -1.95 \cdot 10^{-79}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(A - C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-16}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(C - A\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \]

Alternative 16
Accuracy	17.6%
Cost	8844

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -4 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-78}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-12}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(C - A\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 17
Accuracy	17.8%
Cost	8844

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -1.28 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -2.05 \cdot 10^{-78}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(A - C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(C - A\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 18
Accuracy	15.7%
Cost	8716

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;C \leq -3.7 \cdot 10^{+258}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;C \leq -4.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + \left(C + C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 1.3 \cdot 10^{-150}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \end{array} \]

Alternative 19
Accuracy	17.5%
Cost	8716

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;A \leq -4 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -4.9 \cdot 10^{-79}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + \left(C + C\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 20
Accuracy	15.2%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;C \leq -3.7 \cdot 10^{+258}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;C \leq -3.7 \cdot 10^{+32}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + \left(C + C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \end{array} \]

Alternative 21
Accuracy	14.0%
Cost	8332

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;A \leq -1.9 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-201}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(B \cdot \left(B \cdot F\right)\right) \cdot \left(A + \left(C + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 22
Accuracy	14.0%
Cost	8204

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;A \leq -1.15 \cdot 10^{+158}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-201}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;A \leq 1.88 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(2 \cdot \left(C \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 23
Accuracy	10.8%
Cost	8072

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{C}}\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{-125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\frac{1}{B} \cdot \sqrt{F \cdot \left(C + A \cdot \frac{C}{A - C}\right)}\right)\\ \end{array} \]

Alternative 24
Accuracy	14.2%
Cost	7501

\[\begin{array}{l} \mathbf{if}\;C \leq -1.55 \cdot 10^{+142}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{elif}\;C \leq -2.9 \cdot 10^{-289} \lor \neg \left(C \leq 7 \cdot 10^{-118}\right):\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-0.5 \cdot \frac{F \cdot \left(C + C\right)}{C \cdot A}}\\ \end{array} \]

Alternative 25
Accuracy	14.6%
Cost	7053

\[\begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{+142} \lor \neg \left(C \leq -3.2 \cdot 10^{-285}\right) \land C \leq 1.3 \cdot 10^{-117}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \end{array} \]

Alternative 26
Accuracy	11.2%
Cost	6656

\[\sqrt{\frac{-F}{A}} \]

Alternative 27
Accuracy	1.2%
Cost	6592

\[\sqrt{\frac{F}{A}} \]

Reproduce

herbie shell --seed 2023129 
(FPCore (A B C F)
  :name "ABCF->ab-angle b"
  :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))))