ABCF->ab-angle a

Average Accuracy: 17.5% → 36.5%

Time: 1.4min

Precision: binary64

Cost: 46788

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_2 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_3 := \frac{\sqrt{t_0} \cdot \sqrt{F}}{\frac{t_0}{-\sqrt{2 \cdot t_2}}}\\ t_4 := -4 \cdot \left(A \cdot C\right)\\ t_5 := \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_4\right)\right)}\\ t_6 := \mathsf{hypot}\left(B, \sqrt{t_4}\right)\\ t_7 := B \cdot B + t_4\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;\frac{B \cdot \sqrt{2}}{t_6} \cdot \frac{\sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}}{t_6}\\ \mathbf{elif}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-t_5\right)}{t_7}\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-249}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0} \cdot \left(-\sqrt{2 \cdot \left(2 \cdot C\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-183}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-130}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;-\frac{t_5 \cdot \sqrt{t_2}}{t_7}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (fma -4.0 (* A C) (* B B)))
        (t_1 (fma B B (* C (* -4.0 A))))
        (t_2 (+ A (+ C (hypot B (- A C)))))
        (t_3 (/ (* (sqrt t_0) (sqrt F)) (/ t_0 (- (sqrt (* 2.0 t_2))))))
        (t_4 (* -4.0 (* A C)))
        (t_5 (sqrt (* 2.0 (* F (fma B B t_4)))))
        (t_6 (hypot B (sqrt t_4)))
        (t_7 (+ (* B B) t_4)))
   (if (<= B -3.2e+153)
     (*
      (/ (* B (sqrt 2.0)) t_6)
      (/ (sqrt (* F (fma -0.5 (* A (/ A B)) (- A B)))) t_6))
     (if (<= B -4.7e-35)
       t_3
       (if (<= B -4.6e-70)
         (/ (* (sqrt (+ A (+ A (/ (* -0.5 (* B B)) C)))) (- t_5)) t_7)
         (if (<= B -5.2e-194)
           t_3
           (if (<= B -8e-249)
             (/ (* (sqrt (* F t_0)) (- (sqrt (* 2.0 (* 2.0 C))))) t_0)
             (if (<= B 2.8e-256)
               t_3
               (if (<= B 9.2e-183)
                 (- (/ (sqrt (* 2.0 (* t_1 (* F (* 2.0 C))))) t_1))
                 (if (<= B 4.2e-130)
                   (/
                    (- (sqrt (* 2.0 (* (* A (* -4.0 C)) (* F (+ A A))))))
                    t_1)
                   (if (<= B 5.8e+65)
                     (- (/ (* t_5 (sqrt t_2)) t_7))
                     (* (sqrt (/ F B)) (- (sqrt 2.0))))))))))))))

C

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

↓

double code(double A, double B, double C, double F) {
	double t_0 = fma(-4.0, (A * C), (B * B));
	double t_1 = fma(B, B, (C * (-4.0 * A)));
	double t_2 = A + (C + hypot(B, (A - C)));
	double t_3 = (sqrt(t_0) * sqrt(F)) / (t_0 / -sqrt((2.0 * t_2)));
	double t_4 = -4.0 * (A * C);
	double t_5 = sqrt((2.0 * (F * fma(B, B, t_4))));
	double t_6 = hypot(B, sqrt(t_4));
	double t_7 = (B * B) + t_4;
	double tmp;
	if (B <= -3.2e+153) {
		tmp = ((B * sqrt(2.0)) / t_6) * (sqrt((F * fma(-0.5, (A * (A / B)), (A - B)))) / t_6);
	} else if (B <= -4.7e-35) {
		tmp = t_3;
	} else if (B <= -4.6e-70) {
		tmp = (sqrt((A + (A + ((-0.5 * (B * B)) / C)))) * -t_5) / t_7;
	} else if (B <= -5.2e-194) {
		tmp = t_3;
	} else if (B <= -8e-249) {
		tmp = (sqrt((F * t_0)) * -sqrt((2.0 * (2.0 * C)))) / t_0;
	} else if (B <= 2.8e-256) {
		tmp = t_3;
	} else if (B <= 9.2e-183) {
		tmp = -(sqrt((2.0 * (t_1 * (F * (2.0 * C))))) / t_1);
	} else if (B <= 4.2e-130) {
		tmp = -sqrt((2.0 * ((A * (-4.0 * C)) * (F * (A + A))))) / t_1;
	} else if (B <= 5.8e+65) {
		tmp = -((t_5 * sqrt(t_2)) / t_7);
	} else {
		tmp = sqrt((F / B)) * -sqrt(2.0);
	}
	return tmp;
}

Julia

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

↓

function code(A, B, C, F)
	t_0 = fma(-4.0, Float64(A * C), Float64(B * B))
	t_1 = fma(B, B, Float64(C * Float64(-4.0 * A)))
	t_2 = Float64(A + Float64(C + hypot(B, Float64(A - C))))
	t_3 = Float64(Float64(sqrt(t_0) * sqrt(F)) / Float64(t_0 / Float64(-sqrt(Float64(2.0 * t_2)))))
	t_4 = Float64(-4.0 * Float64(A * C))
	t_5 = sqrt(Float64(2.0 * Float64(F * fma(B, B, t_4))))
	t_6 = hypot(B, sqrt(t_4))
	t_7 = Float64(Float64(B * B) + t_4)
	tmp = 0.0
	if (B <= -3.2e+153)
		tmp = Float64(Float64(Float64(B * sqrt(2.0)) / t_6) * Float64(sqrt(Float64(F * fma(-0.5, Float64(A * Float64(A / B)), Float64(A - B)))) / t_6));
	elseif (B <= -4.7e-35)
		tmp = t_3;
	elseif (B <= -4.6e-70)
		tmp = Float64(Float64(sqrt(Float64(A + Float64(A + Float64(Float64(-0.5 * Float64(B * B)) / C)))) * Float64(-t_5)) / t_7);
	elseif (B <= -5.2e-194)
		tmp = t_3;
	elseif (B <= -8e-249)
		tmp = Float64(Float64(sqrt(Float64(F * t_0)) * Float64(-sqrt(Float64(2.0 * Float64(2.0 * C))))) / t_0);
	elseif (B <= 2.8e-256)
		tmp = t_3;
	elseif (B <= 9.2e-183)
		tmp = Float64(-Float64(sqrt(Float64(2.0 * Float64(t_1 * Float64(F * Float64(2.0 * C))))) / t_1));
	elseif (B <= 4.2e-130)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(Float64(A * Float64(-4.0 * C)) * Float64(F * Float64(A + A)))))) / t_1);
	elseif (B <= 5.8e+65)
		tmp = Float64(-Float64(Float64(t_5 * sqrt(t_2)) / t_7));
	else
		tmp = Float64(sqrt(Float64(F / B)) * Float64(-sqrt(2.0)));
	end
	return tmp
end

Wolfram

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

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(-4.0 * N[(A * C), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(B * B + N[(C * N[(-4.0 * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(A + N[(C + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Sqrt[t$95$0], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] / N[(t$95$0 / (-N[Sqrt[N[(2.0 * t$95$2), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-4.0 * N[(A * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Sqrt[N[(2.0 * N[(F * N[(B * B + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[B ^ 2 + N[Sqrt[t$95$4], $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$7 = N[(N[(B * B), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[B, -3.2e+153], N[(N[(N[(B * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision] * N[(N[Sqrt[N[(F * N[(-0.5 * N[(A * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(A - B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.7e-35], t$95$3, If[LessEqual[B, -4.6e-70], N[(N[(N[Sqrt[N[(A + N[(A + N[(N[(-0.5 * N[(B * B), $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-t$95$5)), $MachinePrecision] / t$95$7), $MachinePrecision], If[LessEqual[B, -5.2e-194], t$95$3, If[LessEqual[B, -8e-249], N[(N[(N[Sqrt[N[(F * t$95$0), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(2.0 * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[B, 2.8e-256], t$95$3, If[LessEqual[B, 9.2e-183], (-N[(N[Sqrt[N[(2.0 * N[(t$95$1 * N[(F * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$1), $MachinePrecision]), If[LessEqual[B, 4.2e-130], N[((-N[Sqrt[N[(2.0 * N[(N[(A * N[(-4.0 * C), $MachinePrecision]), $MachinePrecision] * N[(F * N[(A + A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision], If[LessEqual[B, 5.8e+65], (-N[(N[(t$95$5 * N[Sqrt[t$95$2], $MachinePrecision]), $MachinePrecision] / t$95$7), $MachinePrecision]), N[(N[Sqrt[N[(F / B), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -3.2000000000000001e153

   1. Initial program 0.1%

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

   2. Simplified 0.1%

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

      [Start] 0.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in B around -inf 0.1%

      \[\leadsto \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \color{blue}{\left(C + \left(-0.5 \cdot \frac{{\left(A - C\right)}^{2}}{B} + -1 \cdot B\right)\right)}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   4. Taylor expanded in C around 0 1.4%

      \[\leadsto \frac{-\color{blue}{\left(\sqrt{2} \cdot B\right) \cdot \sqrt{F \cdot \left(A + \left(-0.5 \cdot \frac{{A}^{2}}{B} + -1 \cdot B\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   5. Simplified 1.8%

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

      [Start] 1.4	\[ \frac{-\left(\sqrt{2} \cdot B\right) \cdot \sqrt{F \cdot \left(A + \left(-0.5 \cdot \frac{{A}^{2}}{B} + -1 \cdot B\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*l* [=>] 1.4	\[ \frac{-\color{blue}{\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \left(A + \left(-0.5 \cdot \frac{{A}^{2}}{B} + -1 \cdot B\right)\right)}\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 1.4	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \color{blue}{\left(\left(-0.5 \cdot \frac{{A}^{2}}{B} + -1 \cdot B\right) + A\right)}}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+r+ [<=] 1.4	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \color{blue}{\left(-0.5 \cdot \frac{{A}^{2}}{B} + \left(-1 \cdot B + A\right)\right)}}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [<=] 1.4	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \left(-0.5 \cdot \frac{{A}^{2}}{B} + \color{blue}{\left(A + -1 \cdot B\right)}\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      fma-def [=>] 1.4	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \color{blue}{\mathsf{fma}\left(-0.5, \frac{{A}^{2}}{B}, A + -1 \cdot B\right)}}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 1.4	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, \frac{\color{blue}{A \cdot A}}{B}, A + -1 \cdot B\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r/ [<=] 1.8	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, \color{blue}{A \cdot \frac{A}{B}}, A + -1 \cdot B\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      mul-1-neg [=>] 1.8	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A + \color{blue}{\left(-B\right)}\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unsub-neg [=>] 1.8	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, \color{blue}{A - B}\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   6. Applied egg-rr 24.6%

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

      [Start] 1.8	\[ \frac{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      add-sqr-sqrt [=>] 1.8	\[ \frac{\color{blue}{\sqrt{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)} \cdot \sqrt{-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-unprod [=>] 0.2	\[ \frac{\color{blue}{\sqrt{\left(-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)\right) \cdot \left(-\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqr-neg [=>] 0.2	\[ \frac{\sqrt{\color{blue}{\left(\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)\right) \cdot \left(\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-unprod [<=] 0.0	\[ \frac{\color{blue}{\sqrt{\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)} \cdot \sqrt{\sqrt{2} \cdot \left(B \cdot \sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   if -3.2000000000000001e153 < B < -4.7e-35 or -4.60000000000000001e-70 < B < -5.20000000000000003e-194 or -8.00000000000000043e-249 < B < 2.80000000000000023e-256

   1. Initial program 23.1%

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

   2. Simplified 30.9%

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

      [Start] 23.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 39.3%

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

      [Start] 30.9	\[ \frac{-\sqrt{\left(\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 40.0	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 39.3	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 39.3	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   4. Applied egg-rr 40.1%

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

      [Start] 39.3	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      distribute-rgt-neg-in [=>] 39.3	\[ \frac{\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \left(-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-un-lft-identity [=>] 39.3	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \left(-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}\right)}{\color{blue}{1 \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      times-frac [=>] 39.3	\[ \color{blue}{\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      associate-+r+ [=>] 40.1	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(\mathsf{hypot}\left(B, A - C\right) + A\right) + C\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 40.1	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(C + \left(\mathsf{hypot}\left(B, A - C\right) + A\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 40.1	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \color{blue}{\left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   5. Simplified 40.0%

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

      [Start] 40.1	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-*r/ [=>] 40.1	\[ \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      /-rgt-identity [=>] 40.1	\[ \frac{\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}} \cdot \left(-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-/l* [=>] 40.1	\[ \color{blue}{\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}} \]
      *-commutative [=>] 40.1	\[ \frac{\sqrt{\color{blue}{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}} \]
      associate-+r+ [=>] 39.3	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \color{blue}{\left(\left(C + A\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}} \]
      +-commutative [<=] 39.3	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(\color{blue}{\left(A + C\right)} + \mathsf{hypot}\left(B, A - C\right)\right)}}} \]
      associate-+l+ [=>] 40.0	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \color{blue}{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}} \]

   6. Applied egg-rr 38.6%

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

      [Start] 40.0	\[ \frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}} \]
      sqrt-prod [=>] 38.6	\[ \frac{\color{blue}{\sqrt{F} \cdot \sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}} \]
      *-commutative [=>] 38.6	\[ \frac{\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{F}}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}} \]

   if -4.7e-35 < B < -4.60000000000000001e-70

   1. Initial program 28.9%

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

   2. Simplified 28.9%

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

      [Start] 28.9	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 41.4%

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

      [Start] 28.9	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 28.9	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 29.2	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-neg [=>] 29.2	\[ \frac{-\sqrt{2 \cdot \left(\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)} \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-neg-in [=>] 29.2	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 29.2	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot \left(-4\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 29.2	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot \color{blue}{-4}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 29.4	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 29.4	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 41.4	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 41.4%

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

      [Start] 41.4	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 41.4	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 41.4	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in C around -inf 16.0%

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

   6. Simplified 16.0%

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

      [Start] 16.0	\[ \frac{-\sqrt{A + \left(A + -0.5 \cdot \frac{{B}^{2}}{C}\right)} \cdot \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r/ [=>] 16.0	\[ \frac{-\sqrt{A + \left(A + \color{blue}{\frac{-0.5 \cdot {B}^{2}}{C}}\right)} \cdot \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 16.0	\[ \frac{-\sqrt{A + \left(A + \frac{-0.5 \cdot \color{blue}{\left(B \cdot B\right)}}{C}\right)} \cdot \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if -5.20000000000000003e-194 < B < -8.00000000000000043e-249

   1. Initial program 19.4%

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

   2. Simplified 30.7%

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

      [Start] 19.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 32.0%

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

      [Start] 30.7	\[ \frac{-\sqrt{\left(\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 33.6	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 32.0	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 32.0	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   4. Taylor expanded in A around -inf 21.0%

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

   5. Simplified 21.0%

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

      [Start] 21.0	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(2 \cdot C\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-commutative [=>] 21.0	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(C \cdot 2\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   if 2.80000000000000023e-256 < B < 9.20000000000000064e-183

   1. Initial program 17.9%

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

   2. Simplified 24.4%

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

      [Start] 17.9	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around -inf 28.2%

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

   if 9.20000000000000064e-183 < B < 4.20000000000000004e-130

   1. Initial program 20.3%

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

   2. Simplified 29.7%

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

      [Start] 20.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in C around -inf 24.8%

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

   4. Taylor expanded in B around 0 24.3%

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

   5. Simplified 24.3%

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

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

   if 4.20000000000000004e-130 < B < 5.8000000000000001e65

   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 28.7%

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

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

   3. Applied egg-rr 43.2%

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

      [Start] 28.7	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 28.7	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 31.9	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-neg [=>] 31.9	\[ \frac{-\sqrt{2 \cdot \left(\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)} \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-neg-in [=>] 31.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 31.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot \left(-4\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 31.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot \color{blue}{-4}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 32.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 32.3	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 43.2	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 43.2%

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

      [Start] 43.2	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 43.2	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 43.2	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if 5.8000000000000001e65 < B

   1. Initial program 7.6%

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

   2. Simplified 7.6%

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

      [Start] 7.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around 0 13.8%

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

   4. Simplified 13.8%

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

      [Start] 13.8	\[ \frac{-\sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 13.8	\[ \frac{-\sqrt{\color{blue}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 13.8	\[ \frac{-\sqrt{F \cdot \left(C + \sqrt{\color{blue}{B \cdot B} + {C}^{2}}\right)} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 13.8	\[ \frac{-\sqrt{F \cdot \left(C + \sqrt{B \cdot B + \color{blue}{C \cdot C}}\right)} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 13.8	\[ \frac{-\sqrt{F \cdot \left(C + \sqrt{B \cdot B + C \cdot C}\right)} \cdot \color{blue}{\left(B \cdot \sqrt{2}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in C around 0 46.8%

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

   6. Simplified 46.8%

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

      [Start] 46.8	\[ -1 \cdot \left(\sqrt{2} \cdot \sqrt{\frac{F}{B}}\right) \]
      mul-1-neg [=>] 46.8	\[ \color{blue}{-\sqrt{2} \cdot \sqrt{\frac{F}{B}}} \]
      distribute-rgt-neg-in [=>] 46.8	\[ \color{blue}{\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)} \]

3. Recombined 8 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;\frac{B \cdot \sqrt{2}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(A \cdot C\right)}\right)} \cdot \frac{\sqrt{F \cdot \mathsf{fma}\left(-0.5, A \cdot \frac{A}{B}, A - B\right)}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(A \cdot C\right)}\right)}\\ \mathbf{elif}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{F}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)\right)}\right)}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{F}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-249}:\\ \;\;\;\;\frac{\sqrt{F \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \left(-\sqrt{2 \cdot \left(2 \cdot C\right)}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{F}}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-183}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-130}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	41.6%
Cost	149260

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := C \cdot \left(-4 \cdot A\right)\\ t_2 := \mathsf{fma}\left(B, B, t_1\right)\\ t_3 := \frac{t_0}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}\\ t_4 := {B}^{2} + t_1\\ t_5 := \frac{-\sqrt{\left(2 \cdot \left(F \cdot t_4\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_4}\\ \mathbf{if}\;t_5 \leq -1 \cdot 10^{-124}:\\ \;\;\;\;\frac{\sqrt{t_0} \cdot \sqrt{F}}{t_3}\\ \mathbf{elif}\;t_5 \leq 10^{-52}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 2
Accuracy	34.1%
Cost	40520

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\\ t_3 := B \cdot B + t_1\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_5 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_6 := A + \left(C + t_0\right)\\ \mathbf{if}\;A \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-206}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(t_0 + \left(A + C\right)\right)} \cdot \left(\sqrt{t_5} \cdot \left(-\sqrt{F}\right)\right)}{t_5}\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-119}:\\ \;\;\;\;-\frac{t_2 \cdot \sqrt{t_6}}{t_3}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + 0.5 \cdot \frac{B}{\frac{A - C}{B}}\right)} \cdot \left(-t_2\right)}{t_3}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+169}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_1}}{\frac{t_5}{-\sqrt{2 \cdot t_6}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{A + A}\right)}{t_3}\\ \end{array} \]

Alternative 3
Accuracy	35.1%
Cost	33988

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_3 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ \mathbf{if}\;B \leq -2.45 \cdot 10^{-48}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_3}}{\frac{t_3}{-\sqrt{2 \cdot t_2}}}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)} \cdot \sqrt{t_2}}{B \cdot B + t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 4
Accuracy	31.6%
Cost	28248

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_3 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_4 := \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\\ t_5 := \frac{t_2}{-\sqrt{2 \cdot t_3}}\\ t_6 := B \cdot B + t_1\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{B \cdot \left(-\sqrt{F}\right)}{t_5}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-t_4\right)}{t_6}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-105}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_1}}{t_5}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-251}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_2} \cdot \left(-\sqrt{2 \cdot \left(2 \cdot C\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-45}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot t_3\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.26 \cdot 10^{-20}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{A + A}\right)}{t_6}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 5
Accuracy	32.5%
Cost	28248

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := 2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_3 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_4 := F \cdot t_3\\ t_5 := \frac{-\sqrt{t_1 \cdot t_4}}{t_3}\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{B \cdot \left(-\sqrt{F}\right)}{\frac{t_3}{-\sqrt{t_1}}}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_0\right)\right)}\right)}{B \cdot B + t_0}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-101}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-199}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-254}:\\ \;\;\;\;\frac{\sqrt{t_4} \cdot \left(-\sqrt{2 \cdot \left(2 \cdot C\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+52}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 6
Accuracy	29.5%
Cost	27984

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_3 := \frac{-\sqrt{\left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \left(F \cdot t_1\right)}}{t_1}\\ \mathbf{if}\;A \leq -2.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-170}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + 0.5 \cdot \frac{B}{\frac{A - C}{B}}\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_0\right)\right)}\right)}{B \cdot B + t_0}\\ \end{array} \]

Alternative 7
Accuracy	35.1%
Cost	27980

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_2 := -\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_0\right)\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B + t_0}\\ \mathbf{if}\;B \leq -1.95 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \left(B \cdot B\right)}{A}\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 8
Accuracy	31.6%
Cost	27856

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_3 := \frac{t_2}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}\\ t_4 := B \cdot B + t_1\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{B \cdot \left(-\sqrt{F}\right)}{t_3}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\right)}{t_4}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-103}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-199}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_1}}{t_3}\\ \mathbf{elif}\;B \leq -8.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_2} \cdot \left(-\sqrt{2 \cdot \left(2 \cdot C\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-298}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_4\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_4}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 9
Accuracy	31.7%
Cost	27796

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ t_2 := -4 \cdot \left(A \cdot C\right)\\ t_3 := F \cdot \mathsf{fma}\left(B, B, t_2\right)\\ t_4 := B \cdot B + t_2\\ t_5 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_6 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot t_4\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_4}\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{B \cdot \left(-\sqrt{F}\right)}{\frac{t_5}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-\sqrt{2 \cdot t_3}\right)}{t_4}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-194}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_5} \cdot \left(-\sqrt{2 \cdot \left(2 \cdot C\right)}\right)}{t_5}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-240}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 10
Accuracy	31.9%
Cost	27268

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ t_2 := -4 \cdot \left(A \cdot C\right)\\ t_3 := F \cdot \mathsf{fma}\left(B, B, t_2\right)\\ t_4 := B \cdot B + t_2\\ t_5 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot t_4\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_4}\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{B \cdot \left(-\sqrt{F}\right)}{\frac{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}{-\sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-\sqrt{2 \cdot t_3}\right)}{t_4}\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-193}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-132}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{+47}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 11
Accuracy	29.0%
Cost	21640

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ t_2 := -4 \cdot \left(A \cdot C\right)\\ t_3 := B \cdot B + t_2\\ t_4 := F \cdot \mathsf{fma}\left(B, B, t_2\right)\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + \frac{-0.5 \cdot \left(B \cdot B\right)}{C}\right)} \cdot \left(-\sqrt{2 \cdot t_4}\right)}{t_3}\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-240}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{+52}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_3\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 12
Accuracy	26.4%
Cost	21636

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := B \cdot B + t_0\\ t_2 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot t_1\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_1}\\ t_3 := F \cdot \mathsf{fma}\left(B, B, t_0\right)\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_5 := -\frac{\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_4}\\ \mathbf{if}\;B \leq -3.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{A + \left(A + 0.5 \cdot \frac{B}{\frac{A - C}{B}}\right)} \cdot \left(-\sqrt{2 \cdot t_3}\right)}{t_1}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-102}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-280}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-240}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(2 \cdot A\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 13
Accuracy	28.3%
Cost	21396

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ t_2 := -4 \cdot \left(A \cdot C\right)\\ t_3 := B \cdot B + t_2\\ t_4 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot t_3\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_3}\\ t_5 := F \cdot \mathsf{fma}\left(B, B, t_2\right)\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{2 \cdot t_5} \cdot \left(-\sqrt{A + A}\right)}{t_3}\\ \mathbf{elif}\;B \leq -5.1 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_5 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-133}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 14
Accuracy	29.0%
Cost	21396

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := F \cdot \mathsf{fma}\left(B, B, t_1\right)\\ t_3 := B \cdot B + t_1\\ t_4 := -\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{\sqrt{2 \cdot t_2} \cdot \left(-\sqrt{A + A}\right)}{t_3}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-283}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(2 \cdot A\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-186}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_3\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 15
Accuracy	29.8%
Cost	15044

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq 2.3 \cdot 10^{+52}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 16
Accuracy	25.8%
Cost	14736

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)}\\ \mathbf{if}\;B \leq -1.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{\sqrt{B \cdot \left(B \cdot 2\right)} \cdot \left(-\sqrt{F \cdot \left(C - B\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-273}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 17
Accuracy	21.9%
Cost	14604

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(\left(A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(-4 \cdot A\right)\right)}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.85 \cdot 10^{-275}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 18
Accuracy	17.1%
Cost	14084

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{if}\;A \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -16\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-185}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 19
Accuracy	19.1%
Cost	13316

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq 5 \cdot 10^{-39}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 20
Accuracy	10.8%
Cost	8716

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ t_2 := A + \left(A + C\right)\\ \mathbf{if}\;C \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{-244}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right) \cdot t_2\right)}}{t_0}\\ \mathbf{elif}\;C \leq 5.7 \cdot 10^{-53}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot t_2\right)}}{t_0}\\ \end{array} \]

Alternative 21
Accuracy	14.4%
Cost	8712

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-219}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 22
Accuracy	15.4%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 7 \cdot 10^{-86}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 23
Accuracy	10.3%
Cost	8196

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + 2 \cdot A\right)\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 24
Accuracy	9.9%
Cost	8196

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 25
Accuracy	10.8%
Cost	8196

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -7 \cdot 10^{+68}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(-4 \cdot \left(\left(A \cdot C\right) \cdot F\right)\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 26
Accuracy	9.7%
Cost	7940

\[\begin{array}{l} \mathbf{if}\;A \leq 2.1 \cdot 10^{+116}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \sqrt{F \cdot \frac{A}{B \cdot B}}\\ \end{array} \]

Alternative 27
Accuracy	4.3%
Cost	6976

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

Alternative 28
Accuracy	2.9%
Cost	6848

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

Alternative 29
Accuracy	2.9%
Cost	6848

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

Alternative 30
Accuracy	2.8%
Cost	6848

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

Reproduce

herbie shell --seed 2023125 
(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))))