ABCF->ab-angle a

Average Accuracy: 18.8% → 48.9%

Time: 1.1min

Precision: binary64

Cost: 46468

\[ \begin{array}{c}[A, C] = \mathsf{sort}([A, C])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := \left(-4 \cdot C\right) \cdot A\\ t_1 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ t_2 := 2 \cdot \mathsf{fma}\left(B, B, t_0\right)\\ t_3 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -2.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{\sqrt{2 \cdot F}}{\frac{t_1}{B}} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{t_1}\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(\sqrt{t_2} \cdot \sqrt{F}\right) \cdot \left(-\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_2} \cdot \left(-\sqrt{C + C}\right)}{t_3}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{+23}:\\ \;\;\;\;\frac{-\sqrt{t_2 \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

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 (* (* -4.0 C) A))
        (t_1 (hypot B (sqrt t_0)))
        (t_2 (* 2.0 (fma B B t_0)))
        (t_3 (- (* B B) (* 4.0 (* C A)))))
   (if (<= B -2.9e+130)
     (/ (* (/ (sqrt (* 2.0 F)) (/ t_1 B)) (sqrt (+ C (hypot B C)))) t_1)
     (if (<= B -1.12e-40)
       (/
        (* (* (sqrt t_2) (sqrt F)) (- (sqrt (+ C (+ A (hypot B (- A C)))))))
        t_3)
       (if (<= B 2.7e-257)
         (/ (* (sqrt (* F t_2)) (- (sqrt (+ C C)))) t_3)
         (if (<= B 4e+23)
           (/ (- (sqrt (* t_2 (* F (fma 2.0 C (* -0.5 (/ (* B B) A))))))) t_3)
           (* (/ (sqrt F) (sqrt B)) (- (sqrt 2.0)))))))))

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 = (-4.0 * C) * A;
	double t_1 = hypot(B, sqrt(t_0));
	double t_2 = 2.0 * fma(B, B, t_0);
	double t_3 = (B * B) - (4.0 * (C * A));
	double tmp;
	if (B <= -2.9e+130) {
		tmp = ((sqrt((2.0 * F)) / (t_1 / B)) * sqrt((C + hypot(B, C)))) / t_1;
	} else if (B <= -1.12e-40) {
		tmp = ((sqrt(t_2) * sqrt(F)) * -sqrt((C + (A + hypot(B, (A - C)))))) / t_3;
	} else if (B <= 2.7e-257) {
		tmp = (sqrt((F * t_2)) * -sqrt((C + C))) / t_3;
	} else if (B <= 4e+23) {
		tmp = -sqrt((t_2 * (F * fma(2.0, C, (-0.5 * ((B * B) / A)))))) / t_3;
	} else {
		tmp = (sqrt(F) / sqrt(B)) * -sqrt(2.0);
	}
	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(-4.0 * C) * A)
	t_1 = hypot(B, sqrt(t_0))
	t_2 = Float64(2.0 * fma(B, B, t_0))
	t_3 = Float64(Float64(B * B) - Float64(4.0 * Float64(C * A)))
	tmp = 0.0
	if (B <= -2.9e+130)
		tmp = Float64(Float64(Float64(sqrt(Float64(2.0 * F)) / Float64(t_1 / B)) * sqrt(Float64(C + hypot(B, C)))) / t_1);
	elseif (B <= -1.12e-40)
		tmp = Float64(Float64(Float64(sqrt(t_2) * sqrt(F)) * Float64(-sqrt(Float64(C + Float64(A + hypot(B, Float64(A - C))))))) / t_3);
	elseif (B <= 2.7e-257)
		tmp = Float64(Float64(sqrt(Float64(F * t_2)) * Float64(-sqrt(Float64(C + C)))) / t_3);
	elseif (B <= 4e+23)
		tmp = Float64(Float64(-sqrt(Float64(t_2 * Float64(F * fma(2.0, C, Float64(-0.5 * Float64(Float64(B * B) / A))))))) / t_3);
	else
		tmp = Float64(Float64(sqrt(F) / sqrt(B)) * Float64(-sqrt(2.0)));
	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[(-4.0 * C), $MachinePrecision] * A), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[B ^ 2 + N[Sqrt[t$95$0], $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(B * B + t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(B * B), $MachinePrecision] - N[(4.0 * N[(C * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.9e+130], N[(N[(N[(N[Sqrt[N[(2.0 * F), $MachinePrecision]], $MachinePrecision] / N[(t$95$1 / B), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(C + N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[B, -1.12e-40], N[(N[(N[(N[Sqrt[t$95$2], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[N[(C + N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, 2.7e-257], N[(N[(N[Sqrt[N[(F * t$95$2), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(C + C), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, 4e+23], N[((-N[Sqrt[N[(t$95$2 * N[(F * N[(2.0 * C + N[(-0.5 * N[(N[(B * B), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision], N[(N[(N[Sqrt[F], $MachinePrecision] / N[Sqrt[B], $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.8999999999999999e130

   1. Initial program 2.4%

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

   2. Simplified 2.9%

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

      [Start] 2.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around 0 2.4%

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

   4. Simplified 2.8%

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

      [Start] 2.4	\[ \frac{-\sqrt{2 \cdot \left(\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot \left(F \cdot {B}^{2}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 2.4	\[ \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(F \cdot {B}^{2}\right) \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 2.4	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \color{blue}{\left(B \cdot B\right)}\right) \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 2.4	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \sqrt{\color{blue}{{C}^{2} + {B}^{2}}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 2.4	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \sqrt{\color{blue}{C \cdot C} + {B}^{2}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 2.4	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \sqrt{C \cdot C + \color{blue}{B \cdot B}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      hypot-def [=>] 2.8	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \color{blue}{\mathsf{hypot}\left(C, B\right)}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   5. Applied egg-rr 6.3%

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

      [Start] 2.8	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r* [=>] 2.8	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right) \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-prod [=>] 6.3	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      hypot-udef [=>] 4.9	\[ \frac{-\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \color{blue}{\sqrt{C \cdot C + B \cdot B}}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 4.9	\[ \frac{-\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \sqrt{\color{blue}{B \cdot B + C \cdot C}}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      hypot-def [=>] 6.3	\[ \frac{-\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \color{blue}{\mathsf{hypot}\left(B, C\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   6. Simplified 6.3%

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

      [Start] 6.3	\[ \frac{-\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow1/2 [<=] 6.3	\[ \frac{-\color{blue}{{\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}^{0.5}} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 6.3	\[ \frac{-\color{blue}{\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot {\left(2 \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}^{0.5}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow1/2 [=>] 6.3	\[ \frac{-\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \color{blue}{\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   7. Applied egg-rr 33.6%

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

      [Start] 6.3	\[ \frac{-\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      add-sqr-sqrt [=>] 0.0	\[ \frac{\color{blue}{\sqrt{-\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}} \cdot \sqrt{-\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-unprod [=>] 0.1	\[ \frac{\color{blue}{\sqrt{\left(-\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}\right) \cdot \left(-\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqr-neg [=>] 0.1	\[ \frac{\sqrt{\color{blue}{\left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}\right) \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-unprod [<=] 0.2	\[ \frac{\color{blue}{\sqrt{\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}} \cdot \sqrt{\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      add-sqr-sqrt [<=] 0.2	\[ \frac{\color{blue}{\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 0.2	\[ \frac{\color{blue}{\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      add-sqr-sqrt [=>] 0.2	\[ \frac{\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\color{blue}{\sqrt{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]

   8. Simplified 43.7%

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

      [Start] 33.6	\[ \frac{\sqrt{2 \cdot F} \cdot B}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)} \cdot \frac{\sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)} \]
      associate-*r/ [=>] 33.6	\[ \color{blue}{\frac{\frac{\sqrt{2 \cdot F} \cdot B}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)}} \]
      associate-/l* [=>] 43.8	\[ \frac{\color{blue}{\frac{\sqrt{2 \cdot F}}{\frac{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)}{B}}} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)} \]
      associate-*r* [=>] 43.7	\[ \frac{\frac{\sqrt{2 \cdot F}}{\frac{\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(-4 \cdot C\right) \cdot A}}\right)}{B}} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)} \]
      associate-*r* [=>] 43.7	\[ \frac{\frac{\sqrt{2 \cdot F}}{\frac{\mathsf{hypot}\left(B, \sqrt{\left(-4 \cdot C\right) \cdot A}\right)}{B}} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(-4 \cdot C\right) \cdot A}}\right)} \]

   if -2.8999999999999999e130 < B < -1.1200000000000001e-40

   1. Initial program 31.8%

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

   2. Simplified 31.8%

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

      [Start] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 38.5%

      \[\leadsto \frac{-\color{blue}{\left(0 + \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof

      [Start] 31.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      add-sqr-sqrt [=>] 31.8	\[ \frac{-\sqrt{\color{blue}{\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)} \cdot \sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqr-neg [<=] 31.8	\[ \frac{-\sqrt{\color{blue}{\left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right) \cdot \left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-unprod [<=] 0.3	\[ \frac{-\color{blue}{\sqrt{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      add-sqr-sqrt [<=] 1.0	\[ \frac{-\color{blue}{\left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      neg-sub0 [=>] 1.0	\[ \frac{-\color{blue}{\left(0 - \sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sub-neg [=>] 1.0	\[ \frac{-\color{blue}{\left(0 + \left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 38.5%

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

      [Start] 38.5	\[ \frac{-\left(0 + \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      +-lft-identity [=>] 38.5	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 38.5	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 38.5	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+r+ [=>] 38.5	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Applied egg-rr 49.8%

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

      [Start] 38.5	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 38.5	\[ \frac{-\sqrt{\color{blue}{\left(\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 49.3	\[ \frac{-\color{blue}{\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      +-commutative [=>] 49.3	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{\color{blue}{\left(C + A\right)} + \mathsf{hypot}\left(B, A - C\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 49.8	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{\color{blue}{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   6. Applied egg-rr 55.1%

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

      [Start] 49.8	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 55.1	\[ \frac{-\color{blue}{\left(\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot \sqrt{F}\right)} \cdot \sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if -1.1200000000000001e-40 < B < 2.6999999999999999e-257

   1. Initial program 19.1%

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

   2. Simplified 19.1%

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

      [Start] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 26.6%

      \[\leadsto \frac{-\color{blue}{\left(0 + \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof

      [Start] 19.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      add-sqr-sqrt [=>] 19.1	\[ \frac{-\sqrt{\color{blue}{\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)} \cdot \sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqr-neg [<=] 19.1	\[ \frac{-\sqrt{\color{blue}{\left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right) \cdot \left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-unprod [<=] 0.9	\[ \frac{-\color{blue}{\sqrt{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      add-sqr-sqrt [<=] 1.1	\[ \frac{-\color{blue}{\left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      neg-sub0 [=>] 1.1	\[ \frac{-\color{blue}{\left(0 - \sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sub-neg [=>] 1.1	\[ \frac{-\color{blue}{\left(0 + \left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 26.6%

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

      [Start] 26.6	\[ \frac{-\left(0 + \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      +-lft-identity [=>] 26.6	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 26.6	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 26.6	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+r+ [=>] 26.6	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Applied egg-rr 35.9%

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

      [Start] 26.6	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 26.3	\[ \frac{-\sqrt{\color{blue}{\left(\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 33.7	\[ \frac{-\color{blue}{\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      +-commutative [=>] 33.7	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{\color{blue}{\left(C + A\right)} + \mathsf{hypot}\left(B, A - C\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 35.9	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F} \cdot \sqrt{\color{blue}{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   6. Taylor expanded in A around -inf 43.7%

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

   if 2.6999999999999999e-257 < B < 3.9999999999999997e23

   1. Initial program 25.4%

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

   2. Simplified 25.4%

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

      [Start] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 33.0%

      \[\leadsto \frac{-\color{blue}{\left(0 + \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof

      [Start] 25.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      add-sqr-sqrt [=>] 25.4	\[ \frac{-\sqrt{\color{blue}{\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)} \cdot \sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqr-neg [<=] 25.4	\[ \frac{-\sqrt{\color{blue}{\left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right) \cdot \left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-unprod [<=] 0.9	\[ \frac{-\color{blue}{\sqrt{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      add-sqr-sqrt [<=] 1.2	\[ \frac{-\color{blue}{\left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      neg-sub0 [=>] 1.2	\[ \frac{-\color{blue}{\left(0 - \sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sub-neg [=>] 1.2	\[ \frac{-\color{blue}{\left(0 + \left(-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 33.0%

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

      [Start] 33.0	\[ \frac{-\left(0 + \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      +-lft-identity [=>] 33.0	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 33.0	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 33.0	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+r+ [=>] 33.0	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in A around -inf 41.6%

      \[\leadsto \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \color{blue}{\left(2 \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   6. Simplified 41.6%

      \[\leadsto \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \color{blue}{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof

      [Start] 41.6	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-def [=>] 41.6	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \color{blue}{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{{B}^{2}}{A}\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 41.6	\[ \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{\color{blue}{B \cdot B}}{A}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if 3.9999999999999997e23 < B

   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 15.7%

      \[\leadsto \color{blue}{\frac{-\sqrt{\left(2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}} \]
      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. Taylor expanded in A around 0 13.6%

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

   4. Simplified 14.9%

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

      [Start] 13.6	\[ \frac{-\sqrt{2 \cdot \left(\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot \left(F \cdot {B}^{2}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 13.6	\[ \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(F \cdot {B}^{2}\right) \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 13.6	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \color{blue}{\left(B \cdot B\right)}\right) \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 13.6	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \sqrt{\color{blue}{{C}^{2} + {B}^{2}}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 13.6	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \sqrt{\color{blue}{C \cdot C} + {B}^{2}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 13.6	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \sqrt{C \cdot C + \color{blue}{B \cdot B}}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      hypot-def [=>] 14.9	\[ \frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + \color{blue}{\mathsf{hypot}\left(C, B\right)}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   5. Taylor expanded in C around 0 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\sqrt{2} \cdot \sqrt{\frac{F}{B}}\right)} \]

   6. Simplified 45.8%

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

      [Start] 45.8	\[ -1 \cdot \left(\sqrt{2} \cdot \sqrt{\frac{F}{B}}\right) \]
      mul-1-neg [=>] 45.8	\[ \color{blue}{-\sqrt{2} \cdot \sqrt{\frac{F}{B}}} \]
      *-commutative [=>] 45.8	\[ -\color{blue}{\sqrt{\frac{F}{B}} \cdot \sqrt{2}} \]
      distribute-rgt-neg-in [=>] 45.8	\[ \color{blue}{\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)} \]

   7. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\left(\sqrt{F} \cdot \frac{1}{\sqrt{B}}\right)} \cdot \left(-\sqrt{2}\right) \]
      Proof

      No proof available- proof too large to flatten.

   8. Simplified 62.2%

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

      [Start] 62.2	\[ \left(\sqrt{F} \cdot \frac{1}{\sqrt{B}}\right) \cdot \left(-\sqrt{2}\right) \]
      associate-*r/ [=>] 62.2	\[ \color{blue}{\frac{\sqrt{F} \cdot 1}{\sqrt{B}}} \cdot \left(-\sqrt{2}\right) \]
      *-rgt-identity [=>] 62.2	\[ \frac{\color{blue}{\sqrt{F}}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right) \]

3. Recombined 5 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{\sqrt{2 \cdot F}}{\frac{\mathsf{hypot}\left(B, \sqrt{\left(-4 \cdot C\right) \cdot A}\right)}{B}} \cdot \sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{hypot}\left(B, \sqrt{\left(-4 \cdot C\right) \cdot A}\right)}\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(\sqrt{2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)} \cdot \sqrt{F}\right) \cdot \left(-\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\right)} \cdot \left(-\sqrt{C + C}\right)}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{+23}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	52.7%
Cost	155788

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4 \cdot A, C, B \cdot B\right)\\ t_1 := {B}^{2} - C \cdot \left(A \cdot 4\right)\\ t_2 := -\frac{\sqrt{\left(2 \cdot \left(F \cdot t_1\right)\right) \cdot \left(\left(C + A\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_1}\\ t_3 := \frac{\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{t_0}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-192}:\\ \;\;\;\;t_3 \cdot \left(\sqrt{2 \cdot F} \cdot \left(-\sqrt{t_0}\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+132}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3 \cdot \left(-\sqrt{2 \cdot \left(F \cdot t_0\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \frac{-1}{\frac{\sqrt{B}}{\sqrt{F}}}\\ \end{array} \]

Alternative 2
Accuracy	47.5%
Cost	46468

\[\begin{array}{l} t_0 := 2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_2 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ \mathbf{if}\;B \leq -2.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{B \cdot \sqrt{2 \cdot F}}{t_2} \cdot \frac{\sqrt{C + \mathsf{hypot}\left(B, C\right)}}{t_2}\\ \mathbf{elif}\;B \leq -6.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(\sqrt{t_0} \cdot \sqrt{F}\right) \cdot \left(-\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-258}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{C + C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{+21}:\\ \;\;\;\;\frac{-\sqrt{t_0 \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 3
Accuracy	43.9%
Cost	33284

\[\begin{array}{l} t_0 := 2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;\sqrt{2} \cdot \left(\frac{\sqrt{C + \mathsf{hypot}\left(B, C\right)}}{\mathsf{fma}\left(C, -4 \cdot A, B \cdot B\right)} \cdot \left(B \cdot \sqrt{F}\right)\right)\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-258}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{C + C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{+20}:\\ \;\;\;\;\frac{-\sqrt{t_0 \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 4
Accuracy	43.9%
Cost	26884

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\\ t_1 := 2 \cdot t_0\\ t_2 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;\left(B \cdot \sqrt{2 \cdot F}\right) \cdot \frac{\sqrt{C + \mathsf{hypot}\left(B, C\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-257}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_1} \cdot \left(-\sqrt{C + C}\right)}{t_2}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 5
Accuracy	41.3%
Cost	21644

\[\begin{array}{l} t_0 := 2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -6 \cdot 10^{-37}:\\ \;\;\;\;\frac{\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{F \cdot \left(2 \cdot \left(B \cdot B\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-257}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{C + C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{+30}:\\ \;\;\;\;\frac{-\sqrt{t_0 \cdot \left(F \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 6
Accuracy	41.0%
Cost	21260

\[\begin{array}{l} t_0 := 2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -1.75 \cdot 10^{+148}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(B \cdot \left(B \cdot \left(F \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)\right)\right)\right)}}{-\mathsf{fma}\left(C, -4 \cdot A, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 3.45 \cdot 10^{-258}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{C + C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{-\sqrt{t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 7
Accuracy	41.3%
Cost	21128

\[\begin{array}{l} t_0 := 2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\\ t_1 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -8 \cdot 10^{-37}:\\ \;\;\;\;\frac{\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{F \cdot \left(2 \cdot \left(B \cdot B\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 1.72 \cdot 10^{-258}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{C + C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{-\sqrt{t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 8
Accuracy	41.0%
Cost	20808

\[\begin{array}{l} \mathbf{if}\;B \leq -7.4 \cdot 10^{+151}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(B \cdot \left(B \cdot \left(F \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)\right)\right)\right)}}{-\mathsf{fma}\left(C, -4 \cdot A, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 9
Accuracy	41.0%
Cost	19980

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -3.1 \cdot 10^{+144}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 10
Accuracy	37.0%
Cost	14860

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -7.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(B + C\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 11
Accuracy	37.0%
Cost	14732

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -6 \cdot 10^{+139}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.45 \cdot 10^{+38}:\\ \;\;\;\;-\frac{\sqrt{\mathsf{fma}\left(A, -4 \cdot C, B \cdot B\right) \cdot \left(4 \cdot \left(F \cdot C\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(B + C\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 12
Accuracy	29.7%
Cost	14536

\[\begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{+139}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -1.95 \cdot 10^{-62}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(B + C\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 13
Accuracy	26.5%
Cost	14364

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)}}{t_0}\\ t_3 := \frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) - B\right)}}{t_0}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + A\right)}\right)\\ \end{array} \]

Alternative 14
Accuracy	26.9%
Cost	14364

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)}}{t_0}\\ t_3 := \frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -9.2 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) - B\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.72 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.45 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(B + C\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 15
Accuracy	28.1%
Cost	14348

\[\begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-45}:\\ \;\;\;\;-\frac{\sqrt{-2 \cdot \left(F \cdot {B}^{3}\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(B + C\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 16
Accuracy	27.3%
Cost	14152

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -5 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;-\frac{\sqrt{-2 \cdot \left(F \cdot {B}^{3}\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.06 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(\left(C + A\right) + \left(C - A\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(B + C\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 17
Accuracy	27.3%
Cost	9372

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)}}{t_0}\\ t_3 := \frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -1.24 \cdot 10^{-36}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) - B\right)}}{t_0}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{\frac{F}{\frac{B}{2}}}\\ \end{array} \]

Alternative 18
Accuracy	27.0%
Cost	9244

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \left(C + \left(C + A\right)\right)}}{t_0}\\ t_3 := \frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -3.05 \cdot 10^{-43}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(C + A\right) - B\right)}}{t_0}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{\frac{F}{\frac{B}{2}}}\\ \end{array} \]

Alternative 19
Accuracy	25.6%
Cost	8980

\[\begin{array}{l} t_0 := B \cdot B - 4 \cdot \left(C \cdot A\right)\\ t_1 := \frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ t_2 := \frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(C + \left(C + A\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{\frac{F}{\frac{B}{2}}}\\ \end{array} \]

Alternative 20
Accuracy	26.8%
Cost	7944

\[\begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{B \cdot B - 4 \cdot \left(C \cdot A\right)}\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{\frac{F}{\frac{B}{2}}}\\ \end{array} \]

Alternative 21
Accuracy	17.6%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-307}:\\ \;\;\;\;2 \cdot \frac{\sqrt{F \cdot C}}{B}\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{\frac{F}{\frac{B}{2}}}\\ \end{array} \]

Alternative 22
Accuracy	13.8%
Cost	6784

\[-\sqrt{\frac{F}{\frac{B}{2}}} \]

Alternative 23
Accuracy	1.8%
Cost	6720

\[\sqrt{F \cdot \frac{2}{B}} \]

Reproduce

herbie shell --seed 2023146 
(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))))