ABCF->ab-angle a

Average Accuracy: 17.9% → 47.1%

Time: 1.2min

Precision: binary64

Cost: 149772

Math

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

↓

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \mathsf{fma}\left(B, B, t_0\right)\\ t_2 := A \cdot \left(C \cdot -4\right)\\ t_3 := \mathsf{fma}\left(B, B, t_2\right)\\ t_4 := {B}^{2} + t_0\\ t_5 := -\frac{\sqrt{\left(2 \cdot \left(t_4 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_4}\\ t_6 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;t_5 \leq -5 \cdot 10^{-194}:\\ \;\;\;\;\left(-t_6\right) \cdot \frac{\sqrt{2 \cdot t_3} \cdot \sqrt{F}}{t_3}\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{-75}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_6 \cdot \left(-\frac{\sqrt{\left(B \cdot B\right) \cdot \left(2 \cdot F\right) + t_2 \cdot \left(2 \cdot F\right)}}{t_3}\right)\\ \mathbf{else}:\\ \;\;\;\;t_6 \cdot \left(\sqrt{F} \cdot \frac{\sqrt{2}}{B}\right)\\ \end{array} \]

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 (* C (* A -4.0)))
        (t_1 (fma B B t_0))
        (t_2 (* A (* C -4.0)))
        (t_3 (fma B B t_2))
        (t_4 (+ (pow B 2.0) t_0))
        (t_5
         (-
          (/
           (sqrt
            (*
             (* 2.0 (* t_4 F))
             (+ (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0))))))
           t_4)))
        (t_6 (sqrt (+ A (+ C (hypot B (- A C)))))))
   (if (<= t_5 -5e-194)
     (* (- t_6) (/ (* (sqrt (* 2.0 t_3)) (sqrt F)) t_3))
     (if (<= t_5 2e-75)
       (-
        (/
         (sqrt (* 2.0 (* t_1 (* F (fma 2.0 C (/ (* -0.5 (* B B)) A))))))
         t_1))
       (if (<= t_5 INFINITY)
         (* t_6 (- (/ (sqrt (+ (* (* B B) (* 2.0 F)) (* t_2 (* 2.0 F)))) t_3)))
         (* t_6 (* (sqrt F) (/ (sqrt 2.0) B))))))))

C

double code(double A, double B, double C, double F) {
	return -sqrt(((2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) * ((A + C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / (pow(B, 2.0) - ((4.0 * A) * C));
}

↓

double code(double A, double B, double C, double F) {
	double t_0 = C * (A * -4.0);
	double t_1 = fma(B, B, t_0);
	double t_2 = A * (C * -4.0);
	double t_3 = fma(B, B, t_2);
	double t_4 = pow(B, 2.0) + t_0;
	double t_5 = -(sqrt(((2.0 * (t_4 * F)) * ((A + C) + sqrt((pow(B, 2.0) + pow((A - C), 2.0)))))) / t_4);
	double t_6 = sqrt((A + (C + hypot(B, (A - C)))));
	double tmp;
	if (t_5 <= -5e-194) {
		tmp = -t_6 * ((sqrt((2.0 * t_3)) * sqrt(F)) / t_3);
	} else if (t_5 <= 2e-75) {
		tmp = -(sqrt((2.0 * (t_1 * (F * fma(2.0, C, ((-0.5 * (B * B)) / A)))))) / t_1);
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_6 * -(sqrt((((B * B) * (2.0 * F)) + (t_2 * (2.0 * F)))) / t_3);
	} else {
		tmp = t_6 * (sqrt(F) * (sqrt(2.0) / B));
	}
	return tmp;
}

Julia

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

↓

function code(A, B, C, F)
	t_0 = Float64(C * Float64(A * -4.0))
	t_1 = fma(B, B, t_0)
	t_2 = Float64(A * Float64(C * -4.0))
	t_3 = fma(B, B, t_2)
	t_4 = Float64((B ^ 2.0) + t_0)
	t_5 = Float64(-Float64(sqrt(Float64(Float64(2.0 * Float64(t_4 * F)) * Float64(Float64(A + C) + sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0)))))) / t_4))
	t_6 = sqrt(Float64(A + Float64(C + hypot(B, Float64(A - C)))))
	tmp = 0.0
	if (t_5 <= -5e-194)
		tmp = Float64(Float64(-t_6) * Float64(Float64(sqrt(Float64(2.0 * t_3)) * sqrt(F)) / t_3));
	elseif (t_5 <= 2e-75)
		tmp = Float64(-Float64(sqrt(Float64(2.0 * Float64(t_1 * Float64(F * fma(2.0, C, Float64(Float64(-0.5 * Float64(B * B)) / A)))))) / t_1));
	elseif (t_5 <= Inf)
		tmp = Float64(t_6 * Float64(-Float64(sqrt(Float64(Float64(Float64(B * B) * Float64(2.0 * F)) + Float64(t_2 * Float64(2.0 * F)))) / t_3)));
	else
		tmp = Float64(t_6 * Float64(sqrt(F) * Float64(sqrt(2.0) / B)));
	end
	return tmp
end

Wolfram

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

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(B * B + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(B * B + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[Power[B, 2.0], $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$5 = (-N[(N[Sqrt[N[(N[(2.0 * N[(t$95$4 * 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$4), $MachinePrecision])}, Block[{t$95$6 = N[Sqrt[N[(A + N[(C + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$5, -5e-194], N[((-t$95$6) * N[(N[(N[Sqrt[N[(2.0 * t$95$3), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e-75], (-N[(N[Sqrt[N[(2.0 * N[(t$95$1 * N[(F * N[(2.0 * C + N[(N[(-0.5 * N[(B * B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, Infinity], N[(t$95$6 * (-N[(N[Sqrt[N[(N[(N[(B * B), $MachinePrecision] * N[(2.0 * F), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(2.0 * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$3), $MachinePrecision])), $MachinePrecision], N[(t$95$6 * N[(N[Sqrt[F], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 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))) < -5.0000000000000002e-194

   1. Initial program 40.5%

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

   2. Simplified 40.4%

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

      [Start] 40.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 63.8%

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

      [Start] 40.4	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 40.5	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 47.5	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-neg [=>] 47.5	\[ \frac{-\sqrt{2 \cdot \left(\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)} \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-neg-in [=>] 47.5	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 47.5	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot \left(-4\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 47.5	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot \color{blue}{-4}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 47.5	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 47.5	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 63.8	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 63.7%

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

      [Start] 63.8	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 63.8	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 63.7	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot F}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 63.7	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right) \cdot F}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Applied egg-rr 63.6%

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

      [Start] 63.7	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      div-inv [=>] 63.5	\[ \color{blue}{\left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      distribute-rgt-neg-in [=>] 63.5	\[ \color{blue}{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right)\right)} \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 63.5	\[ \color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right)} \]
      *-commutative [=>] 63.5	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\color{blue}{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot 2\right)} \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      associate-*l* [=>] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\color{blue}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      fma-neg [=>] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\right) \]
      distribute-lft-neg-in [=>] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right)}\right) \]
      metadata-eval [=>] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{-4} \cdot \left(A \cdot C\right)\right)}\right) \]
      *-commutative [<=] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)}\right) \]
      associate-*r* [<=] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)}\right) \]

   6. Simplified 63.8%

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

      [Start] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-lft-neg-out [=>] 63.6	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)} \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      associate-*r/ [=>] 63.8	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\color{blue}{\frac{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)} \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}\right) \]
      *-rgt-identity [=>] 63.8	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\color{blue}{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-frac-neg [<=] 63.8	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   7. Applied egg-rr 79.8%

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

      [Start] 63.8	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 63.8	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{\color{blue}{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot 2\right) \cdot F}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      sqrt-prod [=>] 79.8	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot 2} \cdot \sqrt{F}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   if -5.0000000000000002e-194 < (/.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))) < 1.9999999999999999e-75

   1. Initial program 9.2%

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

   2. Simplified 11.4%

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

      [Start] 9.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around -inf 29.1%

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

   4. Simplified 29.1%

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

      [Start] 29.1	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(2 \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      fma-def [=>] 29.1	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \color{blue}{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{{B}^{2}}{A}\right)}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r/ [=>] 29.1	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, \color{blue}{\frac{-0.5 \cdot {B}^{2}}{A}}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 29.1	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \color{blue}{\left(B \cdot B\right)}}{A}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   if 1.9999999999999999e-75 < (/.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 35.3%

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

   2. Simplified 35.3%

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

      [Start] 35.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 82.4%

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

      [Start] 35.3	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 35.3	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 39.3	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-neg [=>] 39.3	\[ \frac{-\sqrt{2 \cdot \left(\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)} \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-neg-in [=>] 39.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 39.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot \left(-4\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 39.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot \color{blue}{-4}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 39.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 39.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 82.4	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 82.1%

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

      [Start] 82.4	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 82.4	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 82.5	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot F}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 82.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right) \cdot F}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Applied egg-rr 81.7%

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

      [Start] 82.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      div-inv [=>] 81.7	\[ \color{blue}{\left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      distribute-rgt-neg-in [=>] 81.7	\[ \color{blue}{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right)\right)} \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 81.7	\[ \color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right)} \]
      *-commutative [=>] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\color{blue}{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot 2\right)} \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      associate-*l* [=>] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\color{blue}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      fma-neg [=>] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\right) \]
      distribute-lft-neg-in [=>] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right)}\right) \]
      metadata-eval [=>] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{-4} \cdot \left(A \cdot C\right)\right)}\right) \]
      *-commutative [<=] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)}\right) \]
      associate-*r* [<=] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)}\right) \]

   6. Simplified 82.1%

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

      [Start] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-lft-neg-out [=>] 81.7	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)} \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      associate-*r/ [=>] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\color{blue}{\frac{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)} \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}\right) \]
      *-rgt-identity [=>] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\color{blue}{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-frac-neg [<=] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   7. Applied egg-rr 82.1%

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

      [Start] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      *-commutative [=>] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{\color{blue}{\left(2 \cdot F\right) \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      fma-udef [=>] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{\left(2 \cdot F\right) \cdot \color{blue}{\left(B \cdot B + A \cdot \left(C \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      distribute-rgt-in [=>] 82.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \frac{-\sqrt{\color{blue}{\left(B \cdot B\right) \cdot \left(2 \cdot F\right) + \left(A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   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 0.0%

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      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. Applied egg-rr 0.1%

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

      [Start] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 0.0	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 0.0	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-neg [=>] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)} \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-neg-in [=>] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot \left(-4\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot \color{blue}{-4}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 0.0	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 0.1	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 0.1%

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

      [Start] 0.1	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 0.1	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 0.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot F}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 0.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right) \cdot F}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Applied egg-rr 0.1%

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

      [Start] 0.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      div-inv [=>] 0.1	\[ \color{blue}{\left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      distribute-rgt-neg-in [=>] 0.1	\[ \color{blue}{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right)\right)} \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 0.1	\[ \color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right)} \]
      *-commutative [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\color{blue}{\left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot 2\right)} \cdot F}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      associate-*l* [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\color{blue}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      fma-neg [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\right) \]
      distribute-lft-neg-in [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right)}\right) \]
      metadata-eval [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{-4} \cdot \left(A \cdot C\right)\right)}\right) \]
      *-commutative [<=] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot -4}\right)}\right) \]
      associate-*r* [<=] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)}\right) \]

   6. Simplified 0.1%

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

      [Start] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-lft-neg-out [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)} \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)} \]
      associate-*r/ [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\color{blue}{\frac{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)} \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}\right) \]
      *-rgt-identity [=>] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\color{blue}{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      distribute-frac-neg [<=] 0.1	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   7. Taylor expanded in B around -inf 21.3%

      \[\leadsto \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(\frac{\sqrt{2}}{B} \cdot \sqrt{F}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-\frac{\sqrt{\left(2 \cdot \left(\left({B}^{2} + C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq -5 \cdot 10^{-194}:\\ \;\;\;\;\left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\right) \cdot \frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \cdot \sqrt{F}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;-\frac{\sqrt{\left(2 \cdot \left(\left({B}^{2} + C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq 2 \cdot 10^{-75}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;-\frac{\sqrt{\left(2 \cdot \left(\left({B}^{2} + C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq \infty:\\ \;\;\;\;\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\frac{\sqrt{\left(B \cdot B\right) \cdot \left(2 \cdot F\right) + \left(A \cdot \left(C \cdot -4\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\sqrt{F} \cdot \frac{\sqrt{2}}{B}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	50.1%
Cost	28104

\[\begin{array}{l} t_0 := A \cdot \left(C \cdot -4\right)\\ t_1 := \frac{\sqrt{2}}{B}\\ t_2 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -2.55 \cdot 10^{+16}:\\ \;\;\;\;t_2 \cdot \left(\sqrt{F} \cdot t_1\right)\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{+57}:\\ \;\;\;\;t_2 \cdot \left(-\frac{\sqrt{\left(B \cdot B\right) \cdot \left(2 \cdot F\right) + t_0 \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, t_0\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(t_1 \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	45.6%
Cost	27984

\[\begin{array}{l} t_0 := \frac{\sqrt{2}}{B}\\ t_1 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_3 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_4 := \sqrt{t_1}\\ t_5 := -\frac{\sqrt{\left(F \cdot t_3\right) \cdot \left(2 \cdot t_1\right)}}{t_3}\\ \mathbf{if}\;B \leq -0.021:\\ \;\;\;\;t_4 \cdot \left(\sqrt{F} \cdot t_0\right)\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-117}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-302}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-25}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4 \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	45.8%
Cost	27984

\[\begin{array}{l} t_0 := \frac{\sqrt{2}}{B}\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_3 := \mathsf{hypot}\left(B, A - C\right)\\ t_4 := A + \left(C + t_3\right)\\ t_5 := \sqrt{t_4}\\ t_6 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.06 \cdot 10^{+17}:\\ \;\;\;\;t_5 \cdot \left(\sqrt{F} \cdot t_0\right)\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;\sqrt{\left(C + \left(A + t_3\right)\right) \cdot \left(t_2 \cdot \left(2 \cdot F\right)\right)} \cdot \frac{-1}{t_2}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-301}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_6 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_6}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-25}:\\ \;\;\;\;-\frac{\sqrt{\left(F \cdot t_1\right) \cdot \left(2 \cdot t_4\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_5 \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	50.0%
Cost	27848

\[\begin{array}{l} t_0 := \frac{\sqrt{2}}{B}\\ t_1 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -6800000000000:\\ \;\;\;\;t_1 \cdot \left(\sqrt{F} \cdot t_0\right)\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \left(-t_1\right)}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	44.2%
Cost	27720

\[\begin{array}{l} t_0 := \frac{\sqrt{2}}{B}\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ t_2 := \sqrt{A + \left(C + t_1\right)}\\ t_3 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -22000000:\\ \;\;\;\;t_2 \cdot \left(\sqrt{F} \cdot t_0\right)\\ \mathbf{elif}\;B \leq -2.55 \cdot 10^{-115}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(\left(A + C\right) + t_1\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-302}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-153}:\\ \;\;\;\;\frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	43.1%
Cost	27088

\[\begin{array}{l} t_0 := \frac{\sqrt{2}}{B}\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_3 := \frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{if}\;B \leq -5.6 \cdot 10^{-23}:\\ \;\;\;\;t_2 \cdot \left(\sqrt{F} \cdot t_0\right)\\ \mathbf{elif}\;B \leq -1.16 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-293}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	38.1%
Cost	26628

\[\begin{array}{l} t_0 := \frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\sqrt{F} \cdot \frac{\sqrt{2}}{B}\right)\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-294}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.04 \cdot 10^{-109}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 8
Accuracy	26.8%
Cost	22360

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\\ \mathbf{if}\;A \leq -4.65 \cdot 10^{+142}:\\ \;\;\;\;\frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(\left(4 \cdot A\right) \cdot C\right) \cdot \left(F \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -3.9 \cdot 10^{+72}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-C}}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{t_1 \cdot \left(-\sqrt{2 \cdot C}\right)}{t_0}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-217}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-104}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 \cdot \left(-\sqrt{2 \cdot A}\right)}{t_0}\\ \end{array} \]

Alternative 9
Accuracy	25.1%
Cost	21656

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(\left(4 \cdot A\right) \cdot C\right) \cdot \left(F \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ t_2 := \sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{if}\;A \leq -1.02 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -9.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-C}}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \left(B \cdot \left(B \cdot F\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)} \cdot \left(-\sqrt{2 \cdot A}\right)}{t_0}\\ \end{array} \]

Alternative 10
Accuracy	25.3%
Cost	21656

\[\begin{array}{l} t_0 := \sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := \sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\\ \mathbf{if}\;A \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;\frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(\left(4 \cdot A\right) \cdot C\right) \cdot \left(F \cdot \left(C \cdot -2\right)\right)}}{t_1}\\ \mathbf{elif}\;A \leq -7.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-C}}\\ \mathbf{elif}\;A \leq -3.9 \cdot 10^{-57}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{2 \cdot C}\right)}{t_1}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-209}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-248}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \left(B \cdot \left(B \cdot F\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{2 \cdot A}\right)}{t_1}\\ \end{array} \]

Alternative 11
Accuracy	26.3%
Cost	21588

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\\ \mathbf{if}\;A \leq -3.25 \cdot 10^{+143}:\\ \;\;\;\;\frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(\left(4 \cdot A\right) \cdot C\right) \cdot \left(F \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -1.02 \cdot 10^{+74}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-C}}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{t_1 \cdot \left(-\sqrt{2 \cdot C}\right)}{t_0}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-218}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-144}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \left(B \cdot B\right)\right)}\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 \cdot \left(-\sqrt{2 \cdot A}\right)}{t_0}\\ \end{array} \]

Alternative 12
Accuracy	25.5%
Cost	21132

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -9.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 13
Accuracy	26.6%
Cost	21132

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{if}\;B \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \left(B \cdot \left(B \cdot F\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-301}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 14
Accuracy	25.7%
Cost	14988

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(F \cdot \left(2 \cdot C\right)\right) \cdot \left(A \cdot \left(C \cdot -4\right) + B \cdot B\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 15
Accuracy	20.9%
Cost	14732

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(\left(4 \cdot A\right) \cdot C\right) \cdot \left(F \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -1.1 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -9.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-C}}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-73}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 16
Accuracy	25.6%
Cost	14732

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ \mathbf{if}\;B \leq -2.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.72 \cdot 10^{-301}:\\ \;\;\;\;\frac{\left(-\sqrt{2}\right) \cdot \sqrt{\left(\left(4 \cdot A\right) \cdot C\right) \cdot \left(F \cdot \left(C \cdot -2\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.65 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 17
Accuracy	24.7%
Cost	13580

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{-70}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) - B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-206}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-109}:\\ \;\;\;\;\frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 18
Accuracy	19.3%
Cost	13188

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := -\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ t_2 := F \cdot t_0\\ \mathbf{if}\;C \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-C}}\\ \mathbf{elif}\;C \leq -5.9 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -1.45 \cdot 10^{-264}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(A + C\right) + \left(A + \left(0.5 \cdot \frac{B \cdot B}{A - C} - C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 19
Accuracy	19.3%
Cost	8848

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -1.85 \cdot 10^{-264}:\\ \;\;\;\;\frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-198}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{+118}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 20
Accuracy	15.5%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;A \leq -5.2 \cdot 10^{-248}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.75 \cdot 10^{-74}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 21
Accuracy	15.8%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -6.8 \cdot 10^{-248}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 4.9 \cdot 10^{-73}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 22
Accuracy	16.7%
Cost	8204

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq 3.5 \cdot 10^{-307}:\\ \;\;\;\;\frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-195}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-99}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 23
Accuracy	14.4%
Cost	7945

\[\begin{array}{l} \mathbf{if}\;F \leq 9.8 \cdot 10^{-307} \lor \neg \left(F \leq 3 \cdot 10^{+205}\right):\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{A \cdot \left(-16 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 24
Accuracy	16.5%
Cost	7940

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 25
Accuracy	15.6%
Cost	7876

\[\begin{array}{l} \mathbf{if}\;F \leq 9.2 \cdot 10^{-307}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-{\left(\left(A \cdot \left(F \cdot \left(A \cdot C\right)\right)\right) \cdot -16\right)}^{0.5}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 26
Accuracy	11.4%
Cost	6656

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

Alternative 27
Accuracy	1.2%
Cost	6592

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

Reproduce

herbie shell --seed 2023126 
(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))))