ABCF->ab-angle a

Average Accuracy: 18.1% → 43.7%

Time: 1.1min

Precision: binary64

Cost: 28644

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := A + \left(C + t_0\right)\\ t_2 := F \cdot t_1\\ t_3 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_4 := \frac{-\sqrt{2}}{B}\\ t_5 := t_4 \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ t_6 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_7 := \frac{-\sqrt{2 \cdot \left(t_6 \cdot t_2\right)}}{t_6}\\ \mathbf{if}\;B \leq -1.2 \cdot 10^{-28}:\\ \;\;\;\;-\frac{\sqrt{t_2}}{\frac{2 \cdot A}{\frac{\sqrt{2}}{\frac{C}{B}}} - \frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-76}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -5.4 \cdot 10^{-129}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;B \leq -2.85 \cdot 10^{-179}:\\ \;\;\;\;-\frac{\sqrt{t_1} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-181}:\\ \;\;\;\;\frac{\sqrt{-16 \cdot \left(C \cdot \left(A \cdot A\right)\right)} \cdot \left(-\sqrt{F}\right)}{t_3}\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_6 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_6}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-286}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-108}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)} \cdot \left(-\sqrt{F \cdot \left(A \cdot \left(C \cdot -4\right)\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{+46}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_4 \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (hypot B (- A C)))
        (t_1 (+ A (+ C t_0)))
        (t_2 (* F t_1))
        (t_3 (fma -4.0 (* A C) (* B B)))
        (t_4 (/ (- (sqrt 2.0)) B))
        (t_5 (* t_4 (/ B (/ (sqrt (* C -2.0)) (sqrt F)))))
        (t_6 (fma B B (* C (* A -4.0))))
        (t_7 (/ (- (sqrt (* 2.0 (* t_6 t_2)))) t_6)))
   (if (<= B -1.2e-28)
     (-
      (/ (sqrt t_2) (- (/ (* 2.0 A) (/ (sqrt 2.0) (/ C B))) (/ B (sqrt 2.0)))))
     (if (<= B -3e-76)
       t_5
       (if (<= B -5.4e-129)
         t_7
         (if (<= B -2.85e-179)
           (-
            (/
             (* (sqrt t_1) (sqrt (* 2.0 (* -4.0 (* F (* A C))))))
             (+ (* B B) (* -4.0 (* A C)))))
           (if (<= B -9e-181)
             (/ (* (sqrt (* -16.0 (* C (* A A)))) (- (sqrt F))) t_3)
             (if (<= B -2.3e-251)
               (/ (- (sqrt (* 2.0 (* t_6 (* F (* 2.0 C)))))) t_6)
               (if (<= B -3.5e-286)
                 t_5
                 (if (<= B 8e-108)
                   (/
                    (*
                     (sqrt (* 2.0 (+ C (+ A t_0))))
                     (- (sqrt (* F (* A (* C -4.0))))))
                    t_3)
                   (if (<= B 1.75e+46)
                     t_7
                     (* t_4 (* (sqrt F) (sqrt (+ C (hypot C 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 = hypot(B, (A - C));
	double t_1 = A + (C + t_0);
	double t_2 = F * t_1;
	double t_3 = fma(-4.0, (A * C), (B * B));
	double t_4 = -sqrt(2.0) / B;
	double t_5 = t_4 * (B / (sqrt((C * -2.0)) / sqrt(F)));
	double t_6 = fma(B, B, (C * (A * -4.0)));
	double t_7 = -sqrt((2.0 * (t_6 * t_2))) / t_6;
	double tmp;
	if (B <= -1.2e-28) {
		tmp = -(sqrt(t_2) / (((2.0 * A) / (sqrt(2.0) / (C / B))) - (B / sqrt(2.0))));
	} else if (B <= -3e-76) {
		tmp = t_5;
	} else if (B <= -5.4e-129) {
		tmp = t_7;
	} else if (B <= -2.85e-179) {
		tmp = -((sqrt(t_1) * sqrt((2.0 * (-4.0 * (F * (A * C)))))) / ((B * B) + (-4.0 * (A * C))));
	} else if (B <= -9e-181) {
		tmp = (sqrt((-16.0 * (C * (A * A)))) * -sqrt(F)) / t_3;
	} else if (B <= -2.3e-251) {
		tmp = -sqrt((2.0 * (t_6 * (F * (2.0 * C))))) / t_6;
	} else if (B <= -3.5e-286) {
		tmp = t_5;
	} else if (B <= 8e-108) {
		tmp = (sqrt((2.0 * (C + (A + t_0)))) * -sqrt((F * (A * (C * -4.0))))) / t_3;
	} else if (B <= 1.75e+46) {
		tmp = t_7;
	} else {
		tmp = t_4 * (sqrt(F) * sqrt((C + hypot(C, 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 = hypot(B, Float64(A - C))
	t_1 = Float64(A + Float64(C + t_0))
	t_2 = Float64(F * t_1)
	t_3 = fma(-4.0, Float64(A * C), Float64(B * B))
	t_4 = Float64(Float64(-sqrt(2.0)) / B)
	t_5 = Float64(t_4 * Float64(B / Float64(sqrt(Float64(C * -2.0)) / sqrt(F))))
	t_6 = fma(B, B, Float64(C * Float64(A * -4.0)))
	t_7 = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_6 * t_2)))) / t_6)
	tmp = 0.0
	if (B <= -1.2e-28)
		tmp = Float64(-Float64(sqrt(t_2) / Float64(Float64(Float64(2.0 * A) / Float64(sqrt(2.0) / Float64(C / B))) - Float64(B / sqrt(2.0)))));
	elseif (B <= -3e-76)
		tmp = t_5;
	elseif (B <= -5.4e-129)
		tmp = t_7;
	elseif (B <= -2.85e-179)
		tmp = Float64(-Float64(Float64(sqrt(t_1) * sqrt(Float64(2.0 * Float64(-4.0 * Float64(F * Float64(A * C)))))) / Float64(Float64(B * B) + Float64(-4.0 * Float64(A * C)))));
	elseif (B <= -9e-181)
		tmp = Float64(Float64(sqrt(Float64(-16.0 * Float64(C * Float64(A * A)))) * Float64(-sqrt(F))) / t_3);
	elseif (B <= -2.3e-251)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_6 * Float64(F * Float64(2.0 * C)))))) / t_6);
	elseif (B <= -3.5e-286)
		tmp = t_5;
	elseif (B <= 8e-108)
		tmp = Float64(Float64(sqrt(Float64(2.0 * Float64(C + Float64(A + t_0)))) * Float64(-sqrt(Float64(F * Float64(A * Float64(C * -4.0)))))) / t_3);
	elseif (B <= 1.75e+46)
		tmp = t_7;
	else
		tmp = Float64(t_4 * Float64(sqrt(F) * sqrt(Float64(C + hypot(C, 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[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$1 = N[(A + N[(C + t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(F * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(A * C), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[((-N[Sqrt[2.0], $MachinePrecision]) / B), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * N[(B / N[(N[Sqrt[N[(C * -2.0), $MachinePrecision]], $MachinePrecision] / N[Sqrt[F], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(B * B + N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[((-N[Sqrt[N[(2.0 * N[(t$95$6 * t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$6), $MachinePrecision]}, If[LessEqual[B, -1.2e-28], (-N[(N[Sqrt[t$95$2], $MachinePrecision] / N[(N[(N[(2.0 * A), $MachinePrecision] / N[(N[Sqrt[2.0], $MachinePrecision] / N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(B / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[B, -3e-76], t$95$5, If[LessEqual[B, -5.4e-129], t$95$7, If[LessEqual[B, -2.85e-179], (-N[(N[(N[Sqrt[t$95$1], $MachinePrecision] * N[Sqrt[N[(2.0 * N[(-4.0 * N[(F * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(B * B), $MachinePrecision] + N[(-4.0 * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[B, -9e-181], N[(N[(N[Sqrt[N[(-16.0 * N[(C * N[(A * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[F], $MachinePrecision])), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, -2.3e-251], N[((-N[Sqrt[N[(2.0 * N[(t$95$6 * N[(F * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$6), $MachinePrecision], If[LessEqual[B, -3.5e-286], t$95$5, If[LessEqual[B, 8e-108], N[(N[(N[Sqrt[N[(2.0 * N[(C + N[(A + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(F * N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, 1.75e+46], t$95$7, N[(t$95$4 * N[(N[Sqrt[F], $MachinePrecision] * N[Sqrt[N[(C + N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -1.2000000000000001e-28

   1. Initial program 15.7%

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

   2. Simplified 19.7%

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

      [Start] 15.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 25.7%

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

   4. Simplified 25.9%

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

      [Start] 25.7	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{F \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 25.7	\[ \frac{-\color{blue}{\sqrt{F \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+r+ [=>] 26.0	\[ \frac{-\sqrt{F \cdot \color{blue}{\left(\left(\mathsf{hypot}\left(B, A - C\right) + C\right) + A\right)}} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [<=] 26.0	\[ \frac{-\sqrt{F \cdot \left(\color{blue}{\left(C + \mathsf{hypot}\left(B, A - C\right)\right)} + A\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+l+ [=>] 25.9	\[ \frac{-\sqrt{F \cdot \color{blue}{\left(C + \left(\mathsf{hypot}\left(B, A - C\right) + A\right)\right)}} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   5. Applied egg-rr 29.7%

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

   6. Simplified 29.9%

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

      [Start] 29.7	\[ \frac{-\left(\sqrt{\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 29.7	\[ \frac{-\left(\sqrt{\color{blue}{\left(C + A\right) + \mathsf{hypot}\left(B, A - C\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+l+ [=>] 29.9	\[ \frac{-\left(\sqrt{\color{blue}{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   7. Applied egg-rr 26.0%

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

   8. Simplified 26.0%

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

      [Start] 26.0	\[ \frac{-\sqrt{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot F}}{1} \cdot \frac{\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r/ [=>] 26.0	\[ \color{blue}{\frac{\frac{-\sqrt{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot F}}{1} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}} \]
      /-rgt-identity [=>] 26.0	\[ \frac{\color{blue}{\left(-\sqrt{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot F}\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-/l* [=>] 26.0	\[ \color{blue}{\frac{-\sqrt{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot F}}{\frac{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}}} \]
      *-commutative [=>] 26.0	\[ \frac{-\sqrt{\color{blue}{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\frac{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      *-commutative [=>] 26.0	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot -4\right) \cdot C}\right)}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      associate-*l* [=>] 26.0	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(-4 \cdot C\right)}\right)}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      *-commutative [=>] 26.0	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot -4\right) \cdot C}\right)}}} \]
      associate-*l* [=>] 26.0	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, \color{blue}{A \cdot \left(-4 \cdot C\right)}\right)}}} \]

   9. Taylor expanded in B around -inf 45.9%

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

   10. Simplified 47.4%

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

       [Start] 45.9	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{2 \cdot \frac{A \cdot C}{\sqrt{2} \cdot B} + -1 \cdot \frac{B}{\sqrt{2}}} \]
       mul-1-neg [=>] 45.9	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{2 \cdot \frac{A \cdot C}{\sqrt{2} \cdot B} + \color{blue}{\left(-\frac{B}{\sqrt{2}}\right)}} \]
       unsub-neg [=>] 45.9	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\color{blue}{2 \cdot \frac{A \cdot C}{\sqrt{2} \cdot B} - \frac{B}{\sqrt{2}}}} \]
       *-commutative [=>] 45.9	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\color{blue}{\frac{A \cdot C}{\sqrt{2} \cdot B} \cdot 2} - \frac{B}{\sqrt{2}}} \]
       associate-/l* [=>] 47.4	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\color{blue}{\frac{A}{\frac{\sqrt{2} \cdot B}{C}}} \cdot 2 - \frac{B}{\sqrt{2}}} \]
       associate-*l/ [=>] 47.4	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\color{blue}{\frac{A \cdot 2}{\frac{\sqrt{2} \cdot B}{C}}} - \frac{B}{\sqrt{2}}} \]
       associate-/l* [=>] 47.4	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{A \cdot 2}{\color{blue}{\frac{\sqrt{2}}{\frac{C}{B}}}} - \frac{B}{\sqrt{2}}} \]

   if -1.2000000000000001e-28 < B < -3.00000000000000024e-76 or -2.30000000000000017e-251 < B < -3.49999999999999988e-286

   1. Initial program 26.2%

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

   2. Simplified 34.2%

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

      [Start] 26.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around 0 1.4%

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

   4. Simplified 1.4%

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

      [Start] 1.4	\[ -1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F}\right) \]
      associate-*r* [=>] 1.4	\[ \color{blue}{\left(-1 \cdot \frac{\sqrt{2}}{B}\right) \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F}} \]
      associate-*r/ [=>] 1.4	\[ \color{blue}{\frac{-1 \cdot \sqrt{2}}{B}} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \]
      mul-1-neg [=>] 1.4	\[ \frac{\color{blue}{-\sqrt{2}}}{B} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \]
      *-commutative [=>] 1.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{\color{blue}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}} \]
      +-commutative [=>] 1.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{\color{blue}{{C}^{2} + {B}^{2}}}\right)} \]
      unpow2 [=>] 1.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{\color{blue}{C \cdot C} + {B}^{2}}\right)} \]
      unpow2 [=>] 1.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{C \cdot C + \color{blue}{B \cdot B}}\right)} \]

   5. Taylor expanded in C around -inf 6.2%

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

   6. Simplified 6.2%

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

      [Start] 6.2	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(-0.5 \cdot \frac{{B}^{2}}{C}\right)} \]
      associate-*r/ [=>] 6.2	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \color{blue}{\frac{-0.5 \cdot {B}^{2}}{C}}} \]
      *-commutative [=>] 6.2	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \frac{\color{blue}{{B}^{2} \cdot -0.5}}{C}} \]
      unpow2 [=>] 6.2	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \frac{\color{blue}{\left(B \cdot B\right)} \cdot -0.5}{C}} \]

   7. Applied egg-rr 2.0%

      \[\leadsto \frac{-\sqrt{2}}{B} \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sqrt{F} \cdot B}{\sqrt{C \cdot -2}}\right)} - 1\right)} \]

   8. Simplified 17.4%

      \[\leadsto \frac{-\sqrt{2}}{B} \cdot \color{blue}{\frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}} \]
      Proof

      [Start] 2.0	\[ \frac{-\sqrt{2}}{B} \cdot \left(e^{\mathsf{log1p}\left(\frac{\sqrt{F} \cdot B}{\sqrt{C \cdot -2}}\right)} - 1\right) \]
      expm1-def [=>] 13.5	\[ \frac{-\sqrt{2}}{B} \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sqrt{F} \cdot B}{\sqrt{C \cdot -2}}\right)\right)} \]
      expm1-log1p [=>] 17.0	\[ \frac{-\sqrt{2}}{B} \cdot \color{blue}{\frac{\sqrt{F} \cdot B}{\sqrt{C \cdot -2}}} \]
      *-commutative [=>] 17.0	\[ \frac{-\sqrt{2}}{B} \cdot \frac{\color{blue}{B \cdot \sqrt{F}}}{\sqrt{C \cdot -2}} \]
      associate-/l* [=>] 17.4	\[ \frac{-\sqrt{2}}{B} \cdot \color{blue}{\frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}} \]

   if -3.00000000000000024e-76 < B < -5.39999999999999998e-129 or 8.00000000000000032e-108 < B < 1.74999999999999992e46

   1. Initial program 28.7%

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

   2. Simplified 38.2%

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

      [Start] 28.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   if -5.39999999999999998e-129 < B < -2.85e-179

   1. Initial program 16.1%

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

   2. Simplified 16.1%

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

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

   3. Applied egg-rr 34.5%

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

   4. Simplified 34.5%

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

      [Start] 34.5	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 34.5	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 34.5	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in B around 0 23.6%

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

   6. Simplified 29.1%

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

      [Start] 23.6	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 29.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(-4 \cdot \color{blue}{\left(\left(A \cdot C\right) \cdot F\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 29.1	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(\color{blue}{\left(C \cdot A\right)} \cdot F\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if -2.85e-179 < B < -8.9999999999999998e-181

   1. Initial program 10.6%

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

   2. Simplified 23.3%

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

      [Start] 10.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around inf 21.3%

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

   4. Simplified 23.3%

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

      [Start] 21.3	\[ \frac{-\sqrt{\left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-*r* [=>] 23.3	\[ \frac{-\sqrt{\left(-4 \cdot \color{blue}{\left(\left(A \cdot C\right) \cdot F\right)}\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-*l* [<=] 23.3	\[ \frac{-\sqrt{\color{blue}{\left(\left(-4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [<=] 23.3	\[ \frac{-\sqrt{\color{blue}{\left(F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)\right)} \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 23.3	\[ \frac{-\sqrt{\left(F \cdot \left(-4 \cdot \color{blue}{\left(C \cdot A\right)}\right)\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   5. Applied egg-rr 15.8%

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

   6. Taylor expanded in A around inf 1.7%

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

   7. Simplified 1.7%

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

      [Start] 1.7	\[ \frac{-\sqrt{F} \cdot \sqrt{-16 \cdot \left({A}^{2} \cdot C\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 1.7	\[ \frac{-\sqrt{F} \cdot \sqrt{-16 \cdot \color{blue}{\left(C \cdot {A}^{2}\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      unpow2 [=>] 1.7	\[ \frac{-\sqrt{F} \cdot \sqrt{-16 \cdot \left(C \cdot \color{blue}{\left(A \cdot A\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   if -8.9999999999999998e-181 < B < -2.30000000000000017e-251

   1. Initial program 18.0%

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

   2. Simplified 23.9%

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

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

   3. Taylor expanded in A around -inf 24.0%

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

   if -3.49999999999999988e-286 < B < 8.00000000000000032e-108

   1. Initial program 18.2%

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

   2. Simplified 26.6%

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

      [Start] 18.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around inf 22.5%

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

   4. Simplified 25.2%

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

      [Start] 22.5	\[ \frac{-\sqrt{\left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-*r* [=>] 25.2	\[ \frac{-\sqrt{\left(-4 \cdot \color{blue}{\left(\left(A \cdot C\right) \cdot F\right)}\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-*l* [<=] 25.2	\[ \frac{-\sqrt{\color{blue}{\left(\left(-4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [<=] 25.2	\[ \frac{-\sqrt{\color{blue}{\left(F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)\right)} \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 25.2	\[ \frac{-\sqrt{\left(F \cdot \left(-4 \cdot \color{blue}{\left(C \cdot A\right)}\right)\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   5. Applied egg-rr 30.9%

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

   if 1.74999999999999992e46 < B

   1. Initial program 11.3%

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

   2. Simplified 12.8%

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

      [Start] 11.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around 0 16.4%

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

   4. Simplified 16.4%

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

      [Start] 16.4	\[ -1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F}\right) \]
      associate-*r* [=>] 16.4	\[ \color{blue}{\left(-1 \cdot \frac{\sqrt{2}}{B}\right) \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F}} \]
      associate-*r/ [=>] 16.4	\[ \color{blue}{\frac{-1 \cdot \sqrt{2}}{B}} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \]
      mul-1-neg [=>] 16.4	\[ \frac{\color{blue}{-\sqrt{2}}}{B} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \]
      *-commutative [=>] 16.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{\color{blue}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}} \]
      +-commutative [=>] 16.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{\color{blue}{{C}^{2} + {B}^{2}}}\right)} \]
      unpow2 [=>] 16.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{\color{blue}{C \cdot C} + {B}^{2}}\right)} \]
      unpow2 [=>] 16.4	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{C \cdot C + \color{blue}{B \cdot B}}\right)} \]

   5. Applied egg-rr 70.9%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-28}:\\ \;\;\;\;-\frac{\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{2 \cdot A}{\frac{\sqrt{2}}{\frac{C}{B}}} - \frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-76}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{elif}\;B \leq -5.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq -2.85 \cdot 10^{-179}:\\ \;\;\;\;-\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-181}:\\ \;\;\;\;\frac{\sqrt{-16 \cdot \left(C \cdot \left(A \cdot A\right)\right)} \cdot \left(-\sqrt{F}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-251}:\\ \;\;\;\;\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\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-286}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-108}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \left(-\sqrt{F \cdot \left(A \cdot \left(C \cdot -4\right)\right)}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{+46}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	49.4%
Cost	149516

\[\begin{array}{l} t_0 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := -4 \cdot \left(A \cdot C\right)\\ t_3 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ t_4 := \frac{-\sqrt{\left(2 \cdot \left(t_3 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_3}\\ t_5 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;t_4 \leq -5 \cdot 10^{-192}:\\ \;\;\;\;\frac{\sqrt{F} \cdot \left(-t_0\right)}{\frac{t_5}{\sqrt{2 \cdot t_5}}}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{\sqrt{2 \cdot t_1} \cdot \left(\sqrt{F} \cdot \left(-\sqrt{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{B \cdot B}{A}\right)}\right)\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{t_0 \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_2\right)\right)}\right)}{B \cdot B + t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

Alternative 2
Accuracy	42.0%
Cost	28120

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := A + \left(C + t_0\right)\\ t_2 := \frac{-\sqrt{2}}{B}\\ t_3 := t_2 \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -5 \cdot 10^{-30}:\\ \;\;\;\;-\frac{\sqrt{F \cdot t_1}}{\frac{2 \cdot A}{\frac{\sqrt{2}}{\frac{C}{B}}} - \frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-136}:\\ \;\;\;\;-\frac{\sqrt{t_1} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-11}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)} \cdot \left(-\sqrt{F \cdot \left(A \cdot \left(C \cdot -4\right)\right)}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

Alternative 3
Accuracy	47.1%
Cost	28112

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_3 := \frac{\sqrt{t_2} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\right)}{B \cdot B + t_1}\\ \mathbf{if}\;B \leq -0.0066:\\ \;\;\;\;-\frac{\sqrt{F \cdot t_2}}{\frac{2 \cdot A}{\frac{\sqrt{2}}{\frac{C}{B}}} - \frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

Alternative 4
Accuracy	42.1%
Cost	27332

\[\begin{array}{l} t_0 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_1 := -\frac{\sqrt{t_0} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ t_2 := \frac{-\sqrt{2}}{B}\\ t_3 := t_2 \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;-\frac{\sqrt{F \cdot t_0}}{\frac{2 \cdot A}{\frac{\sqrt{2}}{\frac{C}{B}}} - \frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq -1.52 \cdot 10^{-285}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

Alternative 5
Accuracy	41.9%
Cost	27096

\[\begin{array}{l} t_0 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_1 := -\frac{\sqrt{t_0} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ t_2 := \frac{-\sqrt{2}}{B}\\ t_3 := t_2 \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;-\frac{\sqrt{F \cdot t_0}}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq -2.95 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(\sqrt{F} \cdot \sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \end{array} \]

Alternative 6
Accuracy	37.7%
Cost	21848

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_2 := -\frac{\sqrt{t_1} \cdot \sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ t_3 := \sqrt{F \cdot t_1}\\ t_4 := \frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;-\frac{t_3}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-252}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-289}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_3}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 7
Accuracy	35.0%
Cost	21792

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ t_3 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_4 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_5 := \sqrt{F \cdot t_3}\\ t_6 := \frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{-28}:\\ \;\;\;\;-\frac{t_5}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-166}:\\ \;\;\;\;\sqrt{t_3 \cdot \left(F \cdot \left(A \cdot \left(C \cdot -8\right)\right)\right)} \cdot \frac{-1}{t_4}\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-285}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-242}:\\ \;\;\;\;\frac{\sqrt{-16 \cdot \left(A \cdot \left(C \cdot C\right)\right)} \cdot \left(-\sqrt{F}\right)}{t_4}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-159}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_0\right)\right)} \cdot \left(-\sqrt{A + A}\right)}{B \cdot B + t_0}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_5}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 8
Accuracy	35.3%
Cost	21792

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ t_3 := A + \left(C + t_0\right)\\ t_4 := \sqrt{F \cdot t_3}\\ t_5 := \frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ t_6 := -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -8.2 \cdot 10^{-29}:\\ \;\;\;\;-\frac{t_4}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-77}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-166}:\\ \;\;\;\;\sqrt{t_3 \cdot \left(F \cdot \left(A \cdot \left(C \cdot -8\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-286}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;\frac{-\sqrt{F \cdot \left(\left(C + \left(A + t_0\right)\right) \cdot \left(A \cdot \left(2 \cdot \left(C \cdot -4\right)\right)\right)\right)}}{\mathsf{fma}\left(C \cdot -4, A, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-159}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_6\right)\right)} \cdot \left(-\sqrt{A + A}\right)}{B \cdot B + t_6}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_4}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 9
Accuracy	35.7%
Cost	21528

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ t_2 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_3 := \sqrt{F \cdot t_2}\\ t_4 := \frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{if}\;B \leq -2.4 \cdot 10^{-28}:\\ \;\;\;\;-\frac{t_3}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-166}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(F \cdot \left(A \cdot \left(C \cdot -8\right)\right)\right)} \cdot \frac{-1}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-286}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_3}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 10
Accuracy	35.8%
Cost	21264

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -4.6 \cdot 10^{-45}:\\ \;\;\;\;-\frac{t_1}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-290}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_1}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 11
Accuracy	34.2%
Cost	21084

\[\begin{array}{l} t_0 := \sqrt{C \cdot -2}\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ t_3 := \frac{-\sqrt{2}}{B}\\ t_4 := t_3 \cdot \frac{B \cdot \sqrt{F}}{t_0}\\ t_5 := -\frac{\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{if}\;B \leq -4 \cdot 10^{-30}:\\ \;\;\;\;-\frac{t_2}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-176}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -16\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-290}:\\ \;\;\;\;t_3 \cdot \frac{B}{\frac{t_0}{\sqrt{F}}}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-234}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-160}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-33}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_2}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 12
Accuracy	34.0%
Cost	21084

\[\begin{array}{l} t_0 := \sqrt{C \cdot -2}\\ t_1 := \frac{-\sqrt{2}}{B}\\ t_2 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_3 := A \cdot \left(C \cdot C\right)\\ t_4 := \sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ t_5 := t_1 \cdot \frac{B \cdot \sqrt{F}}{t_0}\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;-\frac{t_4}{\frac{-B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-176}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -16\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-286}:\\ \;\;\;\;t_1 \cdot \frac{B}{\frac{t_0}{\sqrt{F}}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-248}:\\ \;\;\;\;\frac{\sqrt{-16 \cdot t_3} \cdot \left(-\sqrt{F}\right)}{t_2}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(F \cdot t_3\right)}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{t_4}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 13
Accuracy	24.7%
Cost	20952

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := \frac{-\sqrt{2}}{B}\\ t_2 := -\frac{\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ t_3 := \sqrt{C \cdot -2}\\ t_4 := t_1 \cdot \frac{B}{\frac{t_3}{\sqrt{F}}}\\ \mathbf{if}\;B \leq -4.1 \cdot 10^{-175}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -16\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -4.9 \cdot 10^{-290}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 3.65 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;t_1 \cdot \frac{B \cdot \sqrt{F}}{t_3}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \end{array} \]

Alternative 14
Accuracy	19.7%
Cost	20168

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -650:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;A \leq 2.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\right)\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-115}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A + C\right) - B\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(\left(A \cdot A\right) \cdot -8\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 15
Accuracy	26.4%
Cost	20168

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{\sqrt{2}}{B}\\ \mathbf{if}\;C \leq -1.25 \cdot 10^{-122}:\\ \;\;\;\;t_1 \cdot \left(\sqrt{F} \cdot \frac{-B}{\sqrt{C \cdot -2}}\right)\\ \mathbf{elif}\;C \leq 2.85 \cdot 10^{-145}:\\ \;\;\;\;t_1 \cdot \left(-\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\right)\\ \mathbf{elif}\;C \leq 1.06 \cdot 10^{+73}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 16
Accuracy	26.8%
Cost	20168

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -9.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \frac{B}{\frac{\sqrt{C \cdot -2}}{\sqrt{F}}}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\right)\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+72}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 17
Accuracy	18.8%
Cost	14480

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -6800000:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 3.1 \cdot 10^{-227}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{B \cdot F}\\ \mathbf{elif}\;C \leq 3 \cdot 10^{-135}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 7.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -16\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 18
Accuracy	18.3%
Cost	14480

\[\begin{array}{l} t_0 := -\frac{\sqrt{-16 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := F \cdot t_1\\ \mathbf{if}\;A \leq -7200:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + C\right)}\right)\\ \mathbf{elif}\;A \leq 3.3 \cdot 10^{-135}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(A + C\right) - B\right)\right)}}{t_1}\\ \mathbf{elif}\;A \leq 1.62 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(\left(A \cdot A\right) \cdot -8\right) \cdot \left(C \cdot F\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_1}\\ \end{array} \]

Alternative 19
Accuracy	18.8%
Cost	13840

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ t_2 := \frac{-\sqrt{2}}{B} \cdot \sqrt{B \cdot F}\\ \mathbf{if}\;C \leq -670000:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.52 \cdot 10^{-93}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 4.3 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A + C\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 20
Accuracy	13.2%
Cost	8716

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.85 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(\left(A \cdot A\right) \cdot -8\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 21
Accuracy	16.7%
Cost	8712

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -2.52 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 7.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A + C\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 22
Accuracy	16.7%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -2.52 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 9 \cdot 10^{-69}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 23
Accuracy	12.2%
Cost	8452

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -2.52 \cdot 10^{-176}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 24
Accuracy	10.7%
Cost	8196

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -4.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + 2 \cdot A\right)\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 25
Accuracy	11.4%
Cost	8196

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -8 \cdot 10^{-30}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 26
Accuracy	8.6%
Cost	7808

\[\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)} \]

Alternative 27
Accuracy	8.6%
Cost	7808

\[-\frac{\sqrt{2 \cdot \left(\left(\left(A \cdot A\right) \cdot -8\right) \cdot \left(C \cdot F\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)} \]

Alternative 28
Accuracy	2.0%
Cost	7680

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

Reproduce

herbie shell --seed 2023122 
(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))))