ABCF->ab-angle a

Average Accuracy: 17.5% → 51.2%

Time: 1.2min

Precision: binary64

Cost: 34912

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

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ t_2 := \sqrt{A + \left(C + t_1\right)}\\ t_3 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_4 := \frac{-\sqrt{\left(2 \cdot \left(F \cdot t_3\right)\right) \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_3}\\ t_5 := \frac{\sqrt{\left(2 \cdot F\right) \cdot t_0}}{t_0}\\ t_6 := \sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\\ t_7 := \left(A \cdot -8\right) \cdot \left(F \cdot C\right)\\ \mathbf{if}\;B \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot t_6\\ \mathbf{elif}\;B \leq -1.95 \cdot 10^{+18}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-t_2\right)}{t_3}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-176}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-248}:\\ \;\;\;\;\left(-\sqrt{2 \cdot C}\right) \cdot t_5\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;\frac{-\sqrt{t_7 \cdot \frac{-0.5}{\frac{A}{B \cdot B}} + t_7 \cdot \left(2 \cdot C\right)}}{t_3}\\ \mathbf{elif}\;B \leq 600:\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)\right)}{t_3}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{+38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{+112}:\\ \;\;\;\;t_5 \cdot \left(-\sqrt{t_1 + \left(A + C\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_6 \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (/
  (-
   (sqrt
    (*
     (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F))
     (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
  (- (pow B 2.0) (* (* 4.0 A) C))))

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (fma A (* C -4.0) (* B B)))
        (t_1 (hypot B (- A C)))
        (t_2 (sqrt (+ A (+ C t_1))))
        (t_3 (- (* B B) (* (* A C) 4.0)))
        (t_4
         (/
          (- (sqrt (* (* 2.0 (* F t_3)) (fma 2.0 C (* (/ (* B B) A) -0.5)))))
          t_3))
        (t_5 (/ (sqrt (* (* 2.0 F) t_0)) t_0))
        (t_6 (* (sqrt (+ A (hypot B A))) (sqrt F)))
        (t_7 (* (* A -8.0) (* F C))))
   (if (<= B -4.3e+117)
     (* (/ (sqrt 2.0) B) t_6)
     (if (<= B -1.95e+18)
       (/ (* (sqrt (* 2.0 (* F (fma B B (* (* A C) -4.0))))) (- t_2)) t_3)
       (if (<= B -8.5e-176)
         t_4
         (if (<= B 9.6e-248)
           (* (- (sqrt (* 2.0 C))) t_5)
           (if (<= B 1.02e-153)
             (/
              (- (sqrt (+ (* t_7 (/ -0.5 (/ A (* B B)))) (* t_7 (* 2.0 C)))))
              t_3)
             (if (<= B 600.0)
               (/
                (*
                 t_2
                 (* (sqrt F) (- (sqrt (* 2.0 (fma B B (* A (* C -4.0))))))))
                t_3)
               (if (<= B 4.2e+38)
                 t_4
                 (if (<= B 7.8e+112)
                   (* t_5 (- (sqrt (+ t_1 (+ A C)))))
                   (* t_6 (/ (- (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 = fma(A, (C * -4.0), (B * B));
	double t_1 = hypot(B, (A - C));
	double t_2 = sqrt((A + (C + t_1)));
	double t_3 = (B * B) - ((A * C) * 4.0);
	double t_4 = -sqrt(((2.0 * (F * t_3)) * fma(2.0, C, (((B * B) / A) * -0.5)))) / t_3;
	double t_5 = sqrt(((2.0 * F) * t_0)) / t_0;
	double t_6 = sqrt((A + hypot(B, A))) * sqrt(F);
	double t_7 = (A * -8.0) * (F * C);
	double tmp;
	if (B <= -4.3e+117) {
		tmp = (sqrt(2.0) / B) * t_6;
	} else if (B <= -1.95e+18) {
		tmp = (sqrt((2.0 * (F * fma(B, B, ((A * C) * -4.0))))) * -t_2) / t_3;
	} else if (B <= -8.5e-176) {
		tmp = t_4;
	} else if (B <= 9.6e-248) {
		tmp = -sqrt((2.0 * C)) * t_5;
	} else if (B <= 1.02e-153) {
		tmp = -sqrt(((t_7 * (-0.5 / (A / (B * B)))) + (t_7 * (2.0 * C)))) / t_3;
	} else if (B <= 600.0) {
		tmp = (t_2 * (sqrt(F) * -sqrt((2.0 * fma(B, B, (A * (C * -4.0))))))) / t_3;
	} else if (B <= 4.2e+38) {
		tmp = t_4;
	} else if (B <= 7.8e+112) {
		tmp = t_5 * -sqrt((t_1 + (A + C)));
	} else {
		tmp = t_6 * (-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 = fma(A, Float64(C * -4.0), Float64(B * B))
	t_1 = hypot(B, Float64(A - C))
	t_2 = sqrt(Float64(A + Float64(C + t_1)))
	t_3 = Float64(Float64(B * B) - Float64(Float64(A * C) * 4.0))
	t_4 = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(F * t_3)) * fma(2.0, C, Float64(Float64(Float64(B * B) / A) * -0.5))))) / t_3)
	t_5 = Float64(sqrt(Float64(Float64(2.0 * F) * t_0)) / t_0)
	t_6 = Float64(sqrt(Float64(A + hypot(B, A))) * sqrt(F))
	t_7 = Float64(Float64(A * -8.0) * Float64(F * C))
	tmp = 0.0
	if (B <= -4.3e+117)
		tmp = Float64(Float64(sqrt(2.0) / B) * t_6);
	elseif (B <= -1.95e+18)
		tmp = Float64(Float64(sqrt(Float64(2.0 * Float64(F * fma(B, B, Float64(Float64(A * C) * -4.0))))) * Float64(-t_2)) / t_3);
	elseif (B <= -8.5e-176)
		tmp = t_4;
	elseif (B <= 9.6e-248)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * C))) * t_5);
	elseif (B <= 1.02e-153)
		tmp = Float64(Float64(-sqrt(Float64(Float64(t_7 * Float64(-0.5 / Float64(A / Float64(B * B)))) + Float64(t_7 * Float64(2.0 * C))))) / t_3);
	elseif (B <= 600.0)
		tmp = Float64(Float64(t_2 * Float64(sqrt(F) * Float64(-sqrt(Float64(2.0 * fma(B, B, Float64(A * Float64(C * -4.0)))))))) / t_3);
	elseif (B <= 4.2e+38)
		tmp = t_4;
	elseif (B <= 7.8e+112)
		tmp = Float64(t_5 * Float64(-sqrt(Float64(t_1 + Float64(A + C)))));
	else
		tmp = Float64(t_6 * Float64(Float64(-sqrt(2.0)) / B));
	end
	return tmp
end

Wolfram

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

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(A * N[(C * -4.0), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(A + N[(C + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(B * B), $MachinePrecision] - N[(N[(A * C), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[((-N[Sqrt[N[(N[(2.0 * N[(F * t$95$3), $MachinePrecision]), $MachinePrecision] * N[(2.0 * C + N[(N[(N[(B * B), $MachinePrecision] / A), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[Sqrt[N[(N[(2.0 * F), $MachinePrecision] * t$95$0), $MachinePrecision]], $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[Sqrt[N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(A * -8.0), $MachinePrecision] * N[(F * C), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.3e+117], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B), $MachinePrecision] * t$95$6), $MachinePrecision], If[LessEqual[B, -1.95e+18], N[(N[(N[Sqrt[N[(2.0 * N[(F * N[(B * B + N[(N[(A * C), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-t$95$2)), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, -8.5e-176], t$95$4, If[LessEqual[B, 9.6e-248], N[((-N[Sqrt[N[(2.0 * C), $MachinePrecision]], $MachinePrecision]) * t$95$5), $MachinePrecision], If[LessEqual[B, 1.02e-153], N[((-N[Sqrt[N[(N[(t$95$7 * N[(-0.5 / N[(A / N[(B * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision], If[LessEqual[B, 600.0], N[(N[(t$95$2 * N[(N[Sqrt[F], $MachinePrecision] * (-N[Sqrt[N[(2.0 * N[(B * B + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, 4.2e+38], t$95$4, If[LessEqual[B, 7.8e+112], N[(t$95$5 * (-N[Sqrt[N[(t$95$1 + N[(A + C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], N[(t$95$6 * N[((-N[Sqrt[2.0], $MachinePrecision]) / B), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -4.29999999999999998e117

   1. Initial program 4.5%

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

   2. Simplified 4.5%

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

      [Start] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 4.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. 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 2.1%

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

      [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	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\color{blue}{F \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}\right) \]
      +-commutative [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)}\right) \]
      unpow2 [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}\right) \]
      unpow2 [=>] 0.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}\right) \]
      hypot-def [=>] 2.1	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}\right) \]

   5. Applied egg-rr 78.4%

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

      [Start] 2.1	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}\right) \]
      add-sqr-sqrt [=>] 2.1	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\color{blue}{\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)} \cdot \sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}}}\right) \]
      sqr-neg [<=] 2.1	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\color{blue}{\left(-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}\right) \cdot \left(-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}\right)}}\right) \]
      sqrt-unprod [<=] 0.5	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\sqrt{-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}} \cdot \sqrt{-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}}}\right) \]
      add-sqr-sqrt [<=] 39.2	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\left(-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}\right)}\right) \]
      sqrt-prod [=>] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\left(-\color{blue}{\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(A, B\right)}}\right)\right) \]
      distribute-rgt-neg-in [=>] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(A, B\right)}\right)}\right) \]

   6. Simplified 78.4%

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

      [Start] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(A, B\right)}\right)\right) \]
      distribute-rgt-neg-out [=>] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\left(-\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(A, B\right)}\right)}\right) \]
      distribute-lft-neg-out [<=] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\left(-\sqrt{F}\right) \cdot \sqrt{A + \mathsf{hypot}\left(A, B\right)}}\right) \]
      *-commutative [=>] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\sqrt{A + \mathsf{hypot}\left(A, B\right)} \cdot \left(-\sqrt{F}\right)}\right) \]
      hypot-def [<=] 22.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \color{blue}{\sqrt{A \cdot A + B \cdot B}}} \cdot \left(-\sqrt{F}\right)\right) \]
      unpow2 [<=] 22.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{\color{blue}{{A}^{2}} + B \cdot B}} \cdot \left(-\sqrt{F}\right)\right) \]
      unpow2 [<=] 22.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{{A}^{2} + \color{blue}{{B}^{2}}}} \cdot \left(-\sqrt{F}\right)\right) \]
      +-commutative [<=] 22.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}} \cdot \left(-\sqrt{F}\right)\right) \]
      unpow2 [=>] 22.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}} \cdot \left(-\sqrt{F}\right)\right) \]
      unpow2 [=>] 22.6	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}} \cdot \left(-\sqrt{F}\right)\right) \]
      hypot-def [=>] 78.4	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \color{blue}{\mathsf{hypot}\left(B, A\right)}} \cdot \left(-\sqrt{F}\right)\right) \]

   if -4.29999999999999998e117 < B < -1.95e18

   1. Initial program 43.6%

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

   2. Simplified 43.6%

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

      [Start] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 80.8%

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

      [Start] 43.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 43.6	\[ \frac{-\sqrt{\color{blue}{\left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right) \cdot \left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 49.7	\[ \frac{-\color{blue}{\sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 49.7	\[ \frac{-\sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 49.7	\[ \frac{-\sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 80.8	\[ \frac{-\sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if -1.95e18 < B < -8.5e-176 or 600 < B < 4.2e38

   1. Initial program 17.8%

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

   2. Simplified 17.8%

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

      [Start] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 17.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Taylor expanded in A around -inf 32.5%

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

   4. Simplified 32.5%

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

      [Start] 32.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(2 \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-def [=>] 32.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \color{blue}{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{{B}^{2}}{A}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 32.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{\color{blue}{B \cdot B}}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if -8.5e-176 < B < 9.60000000000000012e-248

   1. Initial program 19.5%

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

   2. Simplified 19.5%

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

      [Start] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 36.2%

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

      [Start] 19.5	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 19.5	\[ \frac{-\sqrt{\color{blue}{\left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right) \cdot \left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 23.1	\[ \frac{-\color{blue}{\sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 23.9	\[ \frac{-\sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 23.9	\[ \frac{-\sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 36.2	\[ \frac{-\sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Applied egg-rr 36.2%

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

      [Start] 36.2	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      div-inv [=>] 36.2	\[ \color{blue}{\left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      distribute-rgt-neg-in [=>] 36.2	\[ \color{blue}{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}\right)\right)} \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 36.2	\[ \color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right)} \]
      *-commutative [=>] 36.2	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      associate-*l* [=>] 36.2	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right)}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      fma-neg [=>] 36.2	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\right) \]
      distribute-lft-neg-in [=>] 36.2	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right)}\right) \]
      metadata-eval [=>] 36.2	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{-4} \cdot \left(A \cdot C\right)\right)}\right) \]

   5. Simplified 35.1%

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

      [Start] 36.2	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      +-commutative [=>] 36.2	\[ \sqrt{\color{blue}{\left(C + \mathsf{hypot}\left(B, A - C\right)\right) + A}} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      +-commutative [=>] 36.2	\[ \sqrt{\color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + C\right)} + A} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      associate-+l+ [=>] 35.1	\[ \sqrt{\color{blue}{\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)}} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      associate-*r/ [=>] 35.1	\[ \sqrt{\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)} \cdot \color{blue}{\frac{\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   6. Taylor expanded in A around -inf 37.8%

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

   7. Simplified 37.8%

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

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

   if 9.60000000000000012e-248 < B < 1.02e-153

   1. Initial program 24.3%

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

   2. Simplified 24.3%

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

      [Start] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 24.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Taylor expanded in A around -inf 22.2%

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

   4. Simplified 22.2%

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

      [Start] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(2 \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-def [=>] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \color{blue}{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{{B}^{2}}{A}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{\color{blue}{B \cdot B}}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in B around 0 22.2%

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

   6. Simplified 22.2%

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

      [Start] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right) \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \color{blue}{\left(\left(A \cdot C\right) \cdot F\right)}\right)\right) \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   7. Applied egg-rr 22.2%

      \[\leadsto \frac{-\sqrt{\color{blue}{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \frac{-0.5}{\frac{A}{B \cdot B}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Step-by-step derivation

      [Start] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-udef [=>] 22.2	\[ \frac{-\sqrt{\left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \color{blue}{\left(2 \cdot C + -0.5 \cdot \frac{B \cdot B}{A}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-in [=>] 22.2	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \left(2 \cdot C\right) + \left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 22.2	\[ \frac{-\sqrt{\color{blue}{\left(\left(2 \cdot -4\right) \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)} \cdot \left(2 \cdot C\right) + \left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 22.2	\[ \frac{-\sqrt{\left(\left(2 \cdot -4\right) \cdot \color{blue}{\left(A \cdot \left(C \cdot F\right)\right)}\right) \cdot \left(2 \cdot C\right) + \left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 22.2	\[ \frac{-\sqrt{\color{blue}{\left(\left(\left(2 \cdot -4\right) \cdot A\right) \cdot \left(C \cdot F\right)\right)} \cdot \left(2 \cdot C\right) + \left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 22.2	\[ \frac{-\sqrt{\left(\left(\color{blue}{-8} \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \left(2 \cdot \left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 22.2	\[ \frac{-\sqrt{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \color{blue}{\left(\left(2 \cdot -4\right) \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)} \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 22.2	\[ \frac{-\sqrt{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \left(\left(2 \cdot -4\right) \cdot \color{blue}{\left(A \cdot \left(C \cdot F\right)\right)}\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 22.2	\[ \frac{-\sqrt{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \color{blue}{\left(\left(\left(2 \cdot -4\right) \cdot A\right) \cdot \left(C \cdot F\right)\right)} \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 22.2	\[ \frac{-\sqrt{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \left(\left(\color{blue}{-8} \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(-0.5 \cdot \frac{B \cdot B}{A}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      clear-num [=>] 22.2	\[ \frac{-\sqrt{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(-0.5 \cdot \color{blue}{\frac{1}{\frac{A}{B \cdot B}}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      un-div-inv [=>] 22.2	\[ \frac{-\sqrt{\left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \left(2 \cdot C\right) + \left(\left(-8 \cdot A\right) \cdot \left(C \cdot F\right)\right) \cdot \color{blue}{\frac{-0.5}{\frac{A}{B \cdot B}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if 1.02e-153 < B < 600

   1. Initial program 27.6%

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

   2. Simplified 27.6%

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

      [Start] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 37.5%

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

      [Start] 27.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 27.6	\[ \frac{-\sqrt{\color{blue}{\left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right) \cdot \left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 27.7	\[ \frac{-\color{blue}{\sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 28.1	\[ \frac{-\sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 28.1	\[ \frac{-\sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 37.6	\[ \frac{-\sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Applied egg-rr 48.7%

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

      [Start] 37.5	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 37.6	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right) \cdot F}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 48.7	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(\sqrt{2 \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)} \cdot \sqrt{F}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 48.7	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\sqrt{2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)} \cdot \sqrt{F}\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if 4.2e38 < B < 7.79999999999999937e112

   1. Initial program 26.7%

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

   2. Simplified 26.7%

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

      [Start] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Applied egg-rr 66.8%

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

      [Start] 26.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 26.7	\[ \frac{-\sqrt{\color{blue}{\left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right) \cdot \left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 33.1	\[ \frac{-\color{blue}{\sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 33.1	\[ \frac{-\sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 33.1	\[ \frac{-\sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 66.8	\[ \frac{-\sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)} \cdot \sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Applied egg-rr 67.0%

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

      [Start] 66.8	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      div-inv [=>] 66.5	\[ \color{blue}{\left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      distribute-rgt-neg-in [=>] 66.5	\[ \color{blue}{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}\right)\right)} \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 66.9	\[ \color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right)} \]
      *-commutative [=>] 66.9	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      associate-*l* [=>] 66.9	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(C \cdot -4\right)}\right)\right)}\right) \cdot \frac{1}{B \cdot B - 4 \cdot \left(A \cdot C\right)}\right) \]
      fma-neg [=>] 67.0	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\right) \]
      distribute-lft-neg-in [=>] 67.0	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right)}\right) \]
      metadata-eval [=>] 67.0	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, \color{blue}{-4} \cdot \left(A \cdot C\right)\right)}\right) \]

   5. Simplified 67.2%

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

      [Start] 67.0	\[ \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      +-commutative [=>] 67.0	\[ \sqrt{\color{blue}{\left(C + \mathsf{hypot}\left(B, A - C\right)\right) + A}} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      +-commutative [=>] 67.0	\[ \sqrt{\color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + C\right)} + A} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      associate-+l+ [=>] 67.3	\[ \sqrt{\color{blue}{\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)}} \cdot \left(\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot \frac{1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right) \]
      associate-*r/ [=>] 67.2	\[ \sqrt{\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)} \cdot \color{blue}{\frac{\left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right) \cdot 1}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]

   if 7.79999999999999937e112 < B

   1. Initial program 2.8%

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

   2. Simplified 2.8%

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

      [Start] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      +-commutative [=>] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      unpow2 [=>] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
      associate-*l* [=>] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \color{blue}{4 \cdot \left(A \cdot C\right)}} \]
      unpow2 [=>] 2.8	\[ \frac{-\sqrt{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}{\color{blue}{B \cdot B} - 4 \cdot \left(A \cdot C\right)} \]

   3. Taylor expanded in C around 0 6.7%

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

   4. Simplified 42.8%

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

      [Start] 6.7	\[ -1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}\right) \]
      mul-1-neg [=>] 6.7	\[ \color{blue}{-\frac{\sqrt{2}}{B} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}} \]
      distribute-rgt-neg-in [=>] 6.7	\[ \color{blue}{\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}\right)} \]
      *-commutative [=>] 6.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\color{blue}{F \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}\right) \]
      +-commutative [=>] 6.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)}\right) \]
      unpow2 [=>] 6.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}\right) \]
      unpow2 [=>] 6.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}\right) \]
      hypot-def [=>] 42.8	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}\right) \]

   5. Applied egg-rr 76.7%

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

      [Start] 42.8	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}\right) \]
      *-commutative [=>] 42.8	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{\color{blue}{\left(A + \mathsf{hypot}\left(A, B\right)\right) \cdot F}}\right) \]
      sqrt-prod [=>] 76.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\color{blue}{\sqrt{A + \mathsf{hypot}\left(A, B\right)} \cdot \sqrt{F}}\right) \]

   6. Simplified 76.7%

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

      [Start] 76.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \mathsf{hypot}\left(A, B\right)} \cdot \sqrt{F}\right) \]
      hypot-def [<=] 10.3	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \color{blue}{\sqrt{A \cdot A + B \cdot B}}} \cdot \sqrt{F}\right) \]
      unpow2 [<=] 10.3	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{\color{blue}{{A}^{2}} + B \cdot B}} \cdot \sqrt{F}\right) \]
      unpow2 [<=] 10.3	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{{A}^{2} + \color{blue}{{B}^{2}}}} \cdot \sqrt{F}\right) \]
      +-commutative [<=] 10.3	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}} \cdot \sqrt{F}\right) \]
      unpow2 [=>] 10.3	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}} \cdot \sqrt{F}\right) \]
      unpow2 [=>] 10.3	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}} \cdot \sqrt{F}\right) \]
      hypot-def [=>] 76.7	\[ \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{A + \color{blue}{\mathsf{hypot}\left(B, A\right)}} \cdot \sqrt{F}\right) \]

3. Recombined 8 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq -1.95 \cdot 10^{+18}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot \left(B \cdot B - \left(A \cdot C\right) \cdot 4\right)\right)\right) \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-248}:\\ \;\;\;\;\left(-\sqrt{2 \cdot C}\right) \cdot \frac{\sqrt{\left(2 \cdot F\right) \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)}}{\mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(A \cdot -8\right) \cdot \left(F \cdot C\right)\right) \cdot \frac{-0.5}{\frac{A}{B \cdot B}} + \left(\left(A \cdot -8\right) \cdot \left(F \cdot C\right)\right) \cdot \left(2 \cdot C\right)}}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{elif}\;B \leq 600:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)\right)}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot \left(B \cdot B - \left(A \cdot C\right) \cdot 4\right)\right)\right) \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{\sqrt{\left(2 \cdot F\right) \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)}}{\mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\right) \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	52.9%
Cost	34648

\[\begin{array}{l} t_0 := \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)\\ t_1 := \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)\\ t_2 := \mathsf{hypot}\left(B, A - C\right)\\ t_3 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_4 := \sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\\ t_5 := \frac{\sqrt{\left(2 \cdot F\right) \cdot t_0}}{t_0}\\ \mathbf{if}\;B \leq -2.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot t_4\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{+18}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{A + \left(C + t_2\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot t_3\right)\right) \cdot t_1}}{t_3}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-248}:\\ \;\;\;\;\left(-\sqrt{2 \cdot C}\right) \cdot t_5\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;t_5 \cdot \left(-\sqrt{t_2 + \left(A + C\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_4 \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 2
Accuracy	52.9%
Cost	28376

\[\begin{array}{l} t_0 := \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)\\ t_1 := \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)\\ t_2 := \sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\\ t_3 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_4 := \frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}{t_3}\\ \mathbf{if}\;B \leq -8 \cdot 10^{+115}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot t_2\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -5.3 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot t_3\right)\right) \cdot t_1}}{t_3}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;\left(-\sqrt{2 \cdot C}\right) \cdot \frac{\sqrt{\left(2 \cdot F\right) \cdot t_0}}{t_0}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 3
Accuracy	50.0%
Cost	27532

\[\begin{array}{l} t_0 := \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)\\ t_1 := \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)\\ t_2 := \sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\\ t_3 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_4 := 2 \cdot \left(F \cdot t_3\right)\\ t_5 := \frac{-\sqrt{t_4 \cdot t_1}}{t_3}\\ \mathbf{if}\;B \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot t_2\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-248}:\\ \;\;\;\;\left(-\sqrt{2 \cdot C}\right) \cdot \frac{\sqrt{\left(2 \cdot F\right) \cdot t_0}}{t_0}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq 700:\\ \;\;\;\;-\frac{\sqrt{t_4 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 4
Accuracy	45.4%
Cost	27096

\[\begin{array}{l} t_0 := \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)\\ t_1 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_2 := 2 \cdot \left(F \cdot t_1\right)\\ t_3 := \frac{-\sqrt{t_2 \cdot t_0}}{t_1}\\ \mathbf{if}\;B \leq -1.02 \cdot 10^{+22}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -5.3 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{2 \cdot C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot t_0\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4800:\\ \;\;\;\;-\frac{\sqrt{t_2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\right) \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 5
Accuracy	50.0%
Cost	27096

\[\begin{array}{l} t_0 := \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)\\ t_1 := \sqrt{A + \mathsf{hypot}\left(B, A\right)} \cdot \sqrt{F}\\ t_2 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_3 := 2 \cdot \left(F \cdot t_2\right)\\ t_4 := \frac{-\sqrt{t_3 \cdot t_0}}{t_2}\\ \mathbf{if}\;B \leq -2.15 \cdot 10^{+19}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot t_1\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-176}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{2 \cdot C}\right)}{t_2}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot t_0\right)}}{t_2}\\ \mathbf{elif}\;B \leq 420:\\ \;\;\;\;-\frac{\sqrt{t_3 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{+94}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 6
Accuracy	45.3%
Cost	21776

\[\begin{array}{l} t_0 := \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)\\ t_1 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_2 := 2 \cdot \left(F \cdot t_1\right)\\ t_3 := \frac{-\sqrt{t_2 \cdot t_0}}{t_1}\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{2 \cdot C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot t_0\right)}}{t_1}\\ \mathbf{elif}\;B \leq 6800:\\ \;\;\;\;-\frac{\sqrt{t_2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F} \cdot \sqrt{B}}{\frac{B}{-\sqrt{2}}}\\ \end{array} \]

Alternative 7
Accuracy	45.5%
Cost	21260

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_0}\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 10^{-247}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{2 \cdot C}\right)}{t_0}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 45000:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F} \cdot \sqrt{B}}{\frac{B}{-\sqrt{2}}}\\ \end{array} \]

Alternative 8
Accuracy	45.2%
Cost	20504

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_0}\\ \mathbf{if}\;B \leq -2.15 \cdot 10^{+20}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2900:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{F} \cdot \sqrt{B}\right) \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 9
Accuracy	45.2%
Cost	20504

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_0}\\ \mathbf{if}\;B \leq -6.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 10^{-58}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7600:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F} \cdot \sqrt{B}}{\frac{B}{-\sqrt{2}}}\\ \end{array} \]

Alternative 10
Accuracy	45.4%
Cost	20504

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_0}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 47000:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F} \cdot \sqrt{B}}{\frac{B}{-\sqrt{2}}}\\ \end{array} \]

Alternative 11
Accuracy	45.4%
Cost	20504

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_0}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-247}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1550:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{F} \cdot \sqrt{B}}{\frac{B}{-\sqrt{2}}}\\ \end{array} \]

Alternative 12
Accuracy	41.7%
Cost	15768

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ t_2 := \frac{-\sqrt{t_1 \cdot \mathsf{fma}\left(2, C, \frac{B \cdot B}{A} \cdot -0.5\right)}}{t_0}\\ \mathbf{if}\;B \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 72000:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 13
Accuracy	42.9%
Cost	15316

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ \mathbf{if}\;B \leq -49000000:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 10^{-58}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 14
Accuracy	41.4%
Cost	15256

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := \frac{-\sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -120000000000:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-247}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 56:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 15
Accuracy	41.5%
Cost	14932

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := \frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{2 \cdot C} \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 162:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 16
Accuracy	41.1%
Cost	14668

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := \frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{if}\;B \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 18.5:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 17
Accuracy	33.5%
Cost	13448

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+98}:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(A + \left(C - B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 18
Accuracy	41.3%
Cost	13448

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ \mathbf{if}\;B \leq -550000000000:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{-B \cdot F}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(-\sqrt{2}\right) \cdot \sqrt{\frac{F}{B}}\\ \end{array} \]

Alternative 19
Accuracy	32.5%
Cost	8456

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ t_1 := 2 \cdot \left(F \cdot t_0\right)\\ \mathbf{if}\;B \leq -7 \cdot 10^{+97}:\\ \;\;\;\;-\frac{\sqrt{t_1 \cdot \left(A + \left(C - B\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.24 \cdot 10^{+69}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{F \cdot \left(B \cdot 2\right)}}{B}\\ \end{array} \]

Alternative 20
Accuracy	31.9%
Cost	8324

\[\begin{array}{l} t_0 := B \cdot B - \left(A \cdot C\right) \cdot 4\\ \mathbf{if}\;B \leq 3.25 \cdot 10^{+68}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(F \cdot t_0\right)\right) \cdot \left(2 \cdot C\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{F \cdot \left(B \cdot 2\right)}}{B}\\ \end{array} \]

Alternative 21
Accuracy	23.4%
Cost	7812

\[\begin{array}{l} \mathbf{if}\;B \leq 1.35 \cdot 10^{-161}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{F \cdot \left(B \cdot 2\right)}}{B}\\ \end{array} \]

Alternative 22
Accuracy	26.4%
Cost	7812

\[\begin{array}{l} \mathbf{if}\;B \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;\frac{-\sqrt{A \cdot \left(\left(C \cdot \left(F \cdot C\right)\right) \cdot -16\right)}}{B \cdot B - \left(A \cdot C\right) \cdot 4}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{F \cdot \left(B \cdot 2\right)}}{B}\\ \end{array} \]

Alternative 23
Accuracy	13.8%
Cost	6912

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

Alternative 24
Accuracy	1.8%
Cost	6720

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

Reproduce

herbie shell --seed 2023157 
(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))))