ABCF->ab-angle a

Average Accuracy: 18.2% → 48.6%

Time: 1.4min

Precision: binary64

Cost: 108808

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := -\sqrt{F}\\ t_3 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ t_4 := \frac{-\sqrt{\left(2 \cdot \left(t_3 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_3}\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{t_1} \cdot \left(\sqrt{t_1} \cdot t_2\right)\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{\sqrt{F \cdot t_1}}{4 \cdot \left(A \cdot C\right) - B \cdot B} \cdot \sqrt{2 \cdot \left(A + \left(C + t_0\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot t_2\right)\\ \end{array} \]

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 (hypot B (- A C)))
        (t_1 (fma -4.0 (* A C) (* B B)))
        (t_2 (- (sqrt F)))
        (t_3 (- (pow B 2.0) (* (* 4.0 A) C)))
        (t_4
         (/
          (-
           (sqrt
            (*
             (* 2.0 (* t_3 F))
             (+ (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))))))
          t_3)))
   (if (<= t_4 0.0)
     (* (/ (sqrt (* 2.0 (+ C (+ A t_0)))) t_1) (* (sqrt t_1) t_2))
     (if (<= t_4 INFINITY)
       (*
        (/ (sqrt (* F t_1)) (- (* 4.0 (* A C)) (* B B)))
        (sqrt (* 2.0 (+ A (+ C t_0)))))
       (* (/ (sqrt 2.0) B) (* (sqrt (+ A (hypot B A))) t_2))))))

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 = hypot(B, (A - C));
	double t_1 = fma(-4.0, (A * C), (B * B));
	double t_2 = -sqrt(F);
	double t_3 = pow(B, 2.0) - ((4.0 * A) * C);
	double t_4 = -sqrt(((2.0 * (t_3 * F)) * ((A + C) + sqrt((pow(B, 2.0) + pow((A - C), 2.0)))))) / t_3;
	double tmp;
	if (t_4 <= 0.0) {
		tmp = (sqrt((2.0 * (C + (A + t_0)))) / t_1) * (sqrt(t_1) * t_2);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (sqrt((F * t_1)) / ((4.0 * (A * C)) - (B * B))) * sqrt((2.0 * (A + (C + t_0))));
	} else {
		tmp = (sqrt(2.0) / B) * (sqrt((A + hypot(B, A))) * t_2);
	}
	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 = hypot(B, Float64(A - C))
	t_1 = fma(-4.0, Float64(A * C), Float64(B * B))
	t_2 = Float64(-sqrt(F))
	t_3 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	t_4 = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_3 * F)) * Float64(Float64(A + C) + sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0))))))) / t_3)
	tmp = 0.0
	if (t_4 <= 0.0)
		tmp = Float64(Float64(sqrt(Float64(2.0 * Float64(C + Float64(A + t_0)))) / t_1) * Float64(sqrt(t_1) * t_2));
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(sqrt(Float64(F * t_1)) / Float64(Float64(4.0 * Float64(A * C)) - Float64(B * B))) * sqrt(Float64(2.0 * Float64(A + Float64(C + t_0)))));
	else
		tmp = Float64(Float64(sqrt(2.0) / B) * Float64(sqrt(Float64(A + hypot(B, A))) * t_2));
	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[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(A * C), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[Sqrt[F], $MachinePrecision])}, Block[{t$95$3 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$3 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, 0.0], N[(N[(N[Sqrt[N[(2.0 * N[(C + N[(A + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$1), $MachinePrecision] * N[(N[Sqrt[t$95$1], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(N[Sqrt[N[(F * t$95$1), $MachinePrecision]], $MachinePrecision] / N[(N[(4.0 * N[(A * C), $MachinePrecision]), $MachinePrecision] - N[(B * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(2.0 * N[(A + N[(C + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B), $MachinePrecision] * N[(N[Sqrt[N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < -0.0

   1. Initial program 29.9%

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

   2. Simplified 37.8%

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

      [Start] 29.9	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 46.2%

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

      [Start] 37.8	\[ \frac{-\sqrt{\left(\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 47.5	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 47.5	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 46.2	\[ \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 46.2	\[ \frac{-\sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   4. Simplified 47.4%

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

      [Start] 46.2	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 46.2	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 46.2	\[ \frac{-\sqrt{\color{blue}{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 46.2	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, \color{blue}{C \cdot A}, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 47.4	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(\left(\mathsf{hypot}\left(B, A - C\right) + A\right) + C\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 47.4	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(C + \left(\mathsf{hypot}\left(B, A - C\right) + A\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 47.4	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \color{blue}{\left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   5. Applied egg-rr 46.2%

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

      [Start] 47.4	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      distribute-rgt-neg-in [=>] 47.4	\[ \frac{\color{blue}{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-un-lft-identity [=>] 47.4	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\color{blue}{1 \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      times-frac [=>] 47.4	\[ \color{blue}{\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      +-commutative [=>] 47.4	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(A + \mathsf{hypot}\left(B, A - C\right)\right) + C\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 47.4	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + A\right)} + C\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+l+ [=>] 46.2	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 46.2	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \color{blue}{\left(C + A\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [<=] 46.2	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, \color{blue}{C \cdot A}, B \cdot B\right)} \]

   6. Simplified 47.4%

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

      [Start] 46.2	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      /-rgt-identity [=>] 46.2	\[ \color{blue}{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      *-commutative [=>] 46.2	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, \color{blue}{A \cdot C}, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      +-commutative [=>] 46.2	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(C + A\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      associate-+l+ [=>] 47.4	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      *-commutative [=>] 47.4	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, \color{blue}{A \cdot C}, B \cdot B\right)} \]

   7. Applied egg-rr 60.7%

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

      [Start] 47.4	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 60.7	\[ \color{blue}{\left(\sqrt{F} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\right)} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 60.7	\[ \color{blue}{\left(\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{F}\right)} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   if -0.0 < (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < +inf.0

   1. Initial program 38.1%

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

   2. Simplified 58.3%

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

      [Start] 38.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 79.8%

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

      [Start] 58.3	\[ \frac{-\sqrt{\left(\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 79.8	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 79.8	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 79.8	\[ \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \frac{-\sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   4. Simplified 79.8%

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

      [Start] 79.8	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 79.8	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 79.8	\[ \frac{-\sqrt{\color{blue}{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 79.8	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, \color{blue}{C \cdot A}, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 79.8	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(\left(\mathsf{hypot}\left(B, A - C\right) + A\right) + C\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(C + \left(\mathsf{hypot}\left(B, A - C\right) + A\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \color{blue}{\left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   5. Applied egg-rr 79.8%

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

      [Start] 79.8	\[ \frac{-\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      distribute-rgt-neg-in [=>] 79.8	\[ \frac{\color{blue}{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-un-lft-identity [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \cdot \left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\color{blue}{1 \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      times-frac [=>] 79.8	\[ \color{blue}{\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      +-commutative [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(A + \mathsf{hypot}\left(B, A - C\right)\right) + C\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + A\right)} + C\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+l+ [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \color{blue}{\left(C + A\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [<=] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, \color{blue}{C \cdot A}, B \cdot B\right)} \]

   6. Simplified 79.8%

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

      [Start] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      /-rgt-identity [=>] 79.8	\[ \color{blue}{\sqrt{F \cdot \mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      *-commutative [=>] 79.8	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, \color{blue}{A \cdot C}, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(C + A\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      associate-+l+ [=>] 79.8	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)} \]
      *-commutative [=>] 79.8	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, \color{blue}{A \cdot C}, B \cdot B\right)} \]

   7. Applied egg-rr 79.8%

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

      [Start] 79.8	\[ \sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      fma-udef [=>] 79.8	\[ \sqrt{F \cdot \color{blue}{\left(-4 \cdot \left(A \cdot C\right) + B \cdot B\right)}} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      distribute-rgt-in [=>] 79.8	\[ \sqrt{\color{blue}{\left(-4 \cdot \left(A \cdot C\right)\right) \cdot F + \left(B \cdot B\right) \cdot F}} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \sqrt{\color{blue}{\left(B \cdot B\right) \cdot F + \left(-4 \cdot \left(A \cdot C\right)\right) \cdot F}} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   8. Applied egg-rr 79.8%

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

      [Start] 79.8	\[ \sqrt{\left(B \cdot B\right) \cdot F + \left(-4 \cdot \left(A \cdot C\right)\right) \cdot F} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      frac-2neg [=>] 79.8	\[ \sqrt{\left(B \cdot B\right) \cdot F + \left(-4 \cdot \left(A \cdot C\right)\right) \cdot F} \cdot \color{blue}{\frac{-\left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      associate-*r/ [=>] 79.8	\[ \color{blue}{\frac{\sqrt{\left(B \cdot B\right) \cdot F + \left(-4 \cdot \left(A \cdot C\right)\right) \cdot F} \cdot \left(-\left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)\right)}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      distribute-rgt-out [=>] 79.8	\[ \frac{\sqrt{\color{blue}{F \cdot \left(B \cdot B + -4 \cdot \left(A \cdot C\right)\right)}} \cdot \left(-\left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)\right)}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 79.8	\[ \frac{\sqrt{F \cdot \color{blue}{\left(-4 \cdot \left(A \cdot C\right) + B \cdot B\right)}} \cdot \left(-\left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)\right)}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      fma-udef [<=] 79.8	\[ \frac{\sqrt{F \cdot \color{blue}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \cdot \left(-\left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)\right)}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      remove-double-neg [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \color{blue}{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   9. Simplified 79.8%

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

      [Start] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-/l* [=>] 79.8	\[ \color{blue}{\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\frac{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}} \]
      associate-/r/ [=>] 79.8	\[ \color{blue}{\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{-\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}} \]
      neg-sub0 [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\color{blue}{0 - \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      metadata-eval [<=] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\color{blue}{\left(-1 + 1\right)} - \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      unpow2 [<=] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\left(-1 + 1\right) - \mathsf{fma}\left(-4, A \cdot C, \color{blue}{{B}^{2}}\right)} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      fma-udef [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\left(-1 + 1\right) - \color{blue}{\left(-4 \cdot \left(A \cdot C\right) + {B}^{2}\right)}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      associate--r+ [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\color{blue}{\left(\left(-1 + 1\right) - -4 \cdot \left(A \cdot C\right)\right) - {B}^{2}}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      metadata-eval [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\left(\color{blue}{0} - -4 \cdot \left(A \cdot C\right)\right) - {B}^{2}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      neg-sub0 [<=] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\color{blue}{\left(--4 \cdot \left(A \cdot C\right)\right)} - {B}^{2}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      *-commutative [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\left(-\color{blue}{\left(A \cdot C\right) \cdot -4}\right) - {B}^{2}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      distribute-rgt-neg-in [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\color{blue}{\left(A \cdot C\right) \cdot \left(--4\right)} - {B}^{2}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      metadata-eval [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\left(A \cdot C\right) \cdot \color{blue}{4} - {B}^{2}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]
      unpow2 [=>] 79.8	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\left(A \cdot C\right) \cdot 4 - \color{blue}{B \cdot B}} \cdot \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \]

   if +inf.0 < (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))

   1. Initial program 0.0%

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

   2. Simplified 0.9%

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

      [Start] 0.0	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in C around 0 0.6%

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

   4. Simplified 0.6%

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

      [Start] 0.6	\[ -1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}\right) \]
      mul-1-neg [=>] 0.6	\[ \color{blue}{-\frac{\sqrt{2}}{B} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}} \]
      distribute-rgt-neg-in [=>] 0.6	\[ \color{blue}{\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}\right)} \]
      *-commutative [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\color{blue}{F \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}\right) \]
      unpow2 [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)}\right) \]
      unpow2 [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)}\right) \]

   5. Applied egg-rr 27.7%

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

      [Start] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right) \]
      sqrt-prod [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\sqrt{F} \cdot \sqrt{A + \sqrt{B \cdot B + A \cdot A}}}\right) \]
      *-commutative [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\sqrt{A + \sqrt{B \cdot B + A \cdot A}} \cdot \sqrt{F}}\right) \]
      hypot-def [=>] 27.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \color{blue}{\mathsf{hypot}\left(B, A\right)}} \cdot \sqrt{F}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq 0:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \left(\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq \infty:\\ \;\;\;\;\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{4 \cdot \left(A \cdot C\right) - B \cdot B} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	34.6%
Cost	28248

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \frac{\sqrt{2}}{B}\\ t_3 := t_2 \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -3 \cdot 10^{-141}:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-191}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_1} \cdot \left(-\sqrt{2 \cdot \left(C + C\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\left(F \cdot \mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)\right) \cdot \left(2 \cdot A\right)\right|}}{t_4}\\ \mathbf{elif}\;B \leq 66:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{B \cdot \frac{\frac{F}{-2}}{\frac{A}{B}}}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+51}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(A + \left(C + t_0\right)\right)\right)\right)}}{t_4}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Accuracy	42.0%
Cost	27976

\[\begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{+151}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(B \cdot B\right) + F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	35.1%
Cost	27864

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ t_2 := B \cdot \sqrt{F}\\ t_3 := \frac{\sqrt{2}}{B}\\ t_4 := t_3 \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{-142}:\\ \;\;\;\;t_2 \cdot \frac{t_1}{t_0}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{2 \cdot \left(C + C\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-153}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\left(F \cdot \mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)\right) \cdot \left(2 \cdot A\right)\right|}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 220:\\ \;\;\;\;t_3 \cdot \left(-\sqrt{B \cdot \frac{\frac{F}{-2}}{\frac{A}{B}}}\right)\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{-t_1}{t_0} \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 4
Accuracy	42.1%
Cost	27784

\[\begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{+52}:\\ \;\;\;\;\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{4 \cdot \left(A \cdot C\right) - B \cdot B} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	35.6%
Cost	27665

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-175}:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)\right) \cdot \left(2 \cdot \left(A + \left(C + t_0\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-163} \lor \neg \left(B \leq 7500\right):\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\left(F \cdot \mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)\right) \cdot \left(2 \cdot A\right)\right|}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \end{array} \]

Alternative 6
Accuracy	35.2%
Cost	27140

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ \mathbf{if}\;B \leq -9.8 \cdot 10^{-176}:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-192}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)\right) \cdot \left(2 \cdot \left(A + \left(C + t_0\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-152} \lor \neg \left(B \leq 7500\right):\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot t_1\right) \cdot \left(2 \cdot \left(2 \cdot A\right)\right)}}{t_1}\\ \end{array} \]

Alternative 7
Accuracy	32.7%
Cost	26965

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-148}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-149} \lor \neg \left(B \leq 7500\right):\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot t_0\right) \cdot \left(2 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \end{array} \]

Alternative 8
Accuracy	24.5%
Cost	21652

\[\begin{array}{l} t_0 := \frac{\sqrt{2}}{B}\\ t_1 := t_0 \cdot \left(-\sqrt{B \cdot \frac{\frac{F}{-2}}{\frac{A}{B}}}\right)\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;A \leq -2.05 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.03 \cdot 10^{+40}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;A \leq -3300000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-177}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-26}:\\ \;\;\;\;t_0 \cdot \left(-\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{C + \left(A + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(A \cdot C, -4, B \cdot B\right)\right)}\right)}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 9
Accuracy	27.1%
Cost	21396

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 12000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 10
Accuracy	27.6%
Cost	21396

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-152}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-164}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot t_0\right) \cdot \left(2 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 11
Accuracy	26.7%
Cost	21264

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{+27}:\\ \;\;\;\;\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)} \cdot \left(-\sqrt{\frac{2}{B \cdot B}}\right)\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-281}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 12
Accuracy	26.8%
Cost	21264

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-281}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 8100:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot t_0\right) \cdot \left(2 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 13
Accuracy	27.2%
Cost	21264

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(-2 \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(2 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 14
Accuracy	25.7%
Cost	21264

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(-2 \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 255000:\\ \;\;\;\;\frac{-\sqrt{t_1} \cdot \sqrt{2 \cdot \left(C - A \cdot -2\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 15
Accuracy	25.9%
Cost	20616

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, t_0\right) \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -2.35 \cdot 10^{+151}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-149}:\\ \;\;\;\;\sqrt{\frac{2}{B \cdot B}} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)}\right)\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 16
Accuracy	23.5%
Cost	15000

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, t_0\right) \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0}\\ t_3 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;B \leq -5.6 \cdot 10^{+151}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-64}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-291}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-211}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_3\right)}}{t_1}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 17
Accuracy	21.2%
Cost	14488

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}\\ t_2 := \frac{\sqrt{2}}{B}\\ t_3 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{t_1}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-127}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.85 \cdot 10^{-182}:\\ \;\;\;\;\frac{\sqrt{2}}{\frac{B}{t_1}}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_3\right)}}{t_0}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-131}:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 66:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{F \cdot \left(B \cdot \left(B \cdot \frac{-0.5}{A}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 18
Accuracy	21.3%
Cost	14488

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}\\ t_2 := \frac{\sqrt{2}}{B}\\ t_3 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{t_1}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{\sqrt{2}}{\frac{B}{t_1}}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_3\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 66:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{B \cdot \frac{\frac{F}{-2}}{\frac{A}{B}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 19
Accuracy	21.4%
Cost	14488

\[\begin{array}{l} t_0 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := \frac{\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -5.4 \cdot 10^{+150}:\\ \;\;\;\;\frac{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.75 \cdot 10^{-74}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 2.75 \cdot 10^{-204}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_0\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-130}:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 66:\\ \;\;\;\;t_2 \cdot \left(-\sqrt{B \cdot \frac{\frac{F}{-2}}{\frac{A}{B}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 20
Accuracy	21.1%
Cost	14028

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{\sqrt{2}}{\frac{B}{\sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}}}\\ t_2 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;B \leq -2.2 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_2\right)}}{t_0}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 8100:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(C - A\right) - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 21
Accuracy	21.1%
Cost	14028

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{F \cdot \frac{-0.5}{\frac{\frac{A}{B}}{B}}}\\ t_2 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;B \leq -5.1 \cdot 10^{+150}:\\ \;\;\;\;\frac{t_1}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{\sqrt{2}}{\frac{B}{t_1}}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_2\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(C - A\right) - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 22
Accuracy	21.0%
Cost	13712

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-204}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot t_1\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.42 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{B \cdot F}\right)\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C - A\right) - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 23
Accuracy	21.0%
Cost	13448

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -4 \cdot 10^{-117}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right) \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 24
Accuracy	10.0%
Cost	8848

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{if}\;B \leq -4.4 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-212}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(C + \left(A + C\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7500:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{+81}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A \cdot F} \cdot \frac{-2}{B}\\ \end{array} \]

Alternative 25
Accuracy	13.5%
Cost	8712

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ \mathbf{if}\;A \leq -6.7 \cdot 10^{+47}:\\ \;\;\;\;\sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C - A\right) - \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 26
Accuracy	13.2%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;A \leq -3.2 \cdot 10^{+48}:\\ \;\;\;\;\sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(B + \left(A + C\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 27
Accuracy	13.4%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;A \leq -2.6 \cdot 10^{+48}:\\ \;\;\;\;\sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right) \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 28
Accuracy	8.1%
Cost	8328

\[\begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-161}:\\ \;\;\;\;\sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+51}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A \cdot F} \cdot \frac{-2}{B}\\ \end{array} \]

Alternative 29
Accuracy	8.8%
Cost	8328

\[\begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-161}:\\ \;\;\;\;\sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A \cdot F} \cdot \frac{-2}{B}\\ \end{array} \]

Alternative 30
Accuracy	5.3%
Cost	7364

\[\begin{array}{l} \mathbf{if}\;B \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;\sqrt{\frac{\frac{-1}{\frac{\frac{A}{B}}{B \cdot F}}}{B \cdot B}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A \cdot F} \cdot \frac{-2}{B}\\ \end{array} \]

Alternative 31
Accuracy	5.1%
Cost	6980

\[\begin{array}{l} t_0 := \sqrt{A \cdot F}\\ \mathbf{if}\;B \leq -5 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot \frac{t_0}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{-2}{B}\\ \end{array} \]

Alternative 32
Accuracy	3.1%
Cost	6848

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

Reproduce

herbie shell --seed 2023135 
(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))))