ABCF->ab-angle a

Average Error: 52.6 → 35.2

Time: 57.2s

Precision: binary64

Cost: 28112

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{+98}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-184}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

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 B B (* C (* A -4.0))))
        (t_1
         (/
          (*
           (sqrt (+ A (+ C (hypot B (- A C)))))
           (- (sqrt (* F (* 2.0 (fma B B (* A (* C -4.0))))))))
          (+ (* B B) (* -4.0 (* C A))))))
   (if (<= B -6.5e+98)
     (* (sqrt (* 2.0 (+ C (hypot C B)))) (/ (sqrt F) B))
     (if (<= B 2.5e-251)
       t_1
       (if (<= B 8.2e-184)
         (/ (- (sqrt (* 2.0 (* t_0 (* F (* 2.0 C)))))) t_0)
         (if (<= B 2.05e+99) t_1 (* (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(B, B, (C * (A * -4.0)));
	double t_1 = (sqrt((A + (C + hypot(B, (A - C))))) * -sqrt((F * (2.0 * fma(B, B, (A * (C * -4.0))))))) / ((B * B) + (-4.0 * (C * A)));
	double tmp;
	if (B <= -6.5e+98) {
		tmp = sqrt((2.0 * (C + hypot(C, B)))) * (sqrt(F) / B);
	} else if (B <= 2.5e-251) {
		tmp = t_1;
	} else if (B <= 8.2e-184) {
		tmp = -sqrt((2.0 * (t_0 * (F * (2.0 * C))))) / t_0;
	} else if (B <= 2.05e+99) {
		tmp = t_1;
	} 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(B, B, Float64(C * Float64(A * -4.0)))
	t_1 = Float64(Float64(sqrt(Float64(A + Float64(C + hypot(B, Float64(A - C))))) * Float64(-sqrt(Float64(F * Float64(2.0 * fma(B, B, Float64(A * Float64(C * -4.0)))))))) / Float64(Float64(B * B) + Float64(-4.0 * Float64(C * A))))
	tmp = 0.0
	if (B <= -6.5e+98)
		tmp = Float64(sqrt(Float64(2.0 * Float64(C + hypot(C, B)))) * Float64(sqrt(F) / B));
	elseif (B <= 2.5e-251)
		tmp = t_1;
	elseif (B <= 8.2e-184)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_0 * Float64(F * Float64(2.0 * C)))))) / t_0);
	elseif (B <= 2.05e+99)
		tmp = t_1;
	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[(B * B + N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Sqrt[N[(A + N[(C + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(F * N[(2.0 * N[(B * B + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / N[(N[(B * B), $MachinePrecision] + N[(-4.0 * N[(C * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.5e+98], N[(N[Sqrt[N[(2.0 * N[(C + N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-251], t$95$1, If[LessEqual[B, 8.2e-184], N[((-N[Sqrt[N[(2.0 * N[(t$95$0 * N[(F * N[(2.0 * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[B, 2.05e+99], t$95$1, N[(N[Sqrt[N[(F / B), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[2.0], $MachinePrecision])), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.4999999999999999e98

   1. Initial program 60.9

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

   2. Simplified 60.9

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in A around 0 61.0

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

   4. Simplified 61.0

      \[\leadsto \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(C + \sqrt{B \cdot B + C \cdot C}\right) \cdot \left(\left(B \cdot B\right) \cdot F\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C)))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C)))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2))))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (Rewrite<= *-commutative_binary64 (*.f64 F (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error

   5. Applied egg-rr 62.3

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)} \cdot \left(B \cdot \sqrt{F}\right)}{\mathsf{fma}\left(B, B, \left(C \cdot A\right) \cdot -4\right)}\right)} - 1} \]

   6. Simplified 52.1

      \[\leadsto \color{blue}{\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{B \cdot \sqrt{F}}{\mathsf{fma}\left(B, B, \left(-4 \cdot C\right) \cdot A\right)}} \]
      Proof
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 C B)))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 C C) (*.f64 B B))))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 19 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 C 2)) (*.f64 B B)))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 19 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (Rewrite<= unpow2_binary64 (pow.f64 B 2))))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 0 points increase in error, 19 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 19 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (sqrt.f64 (+.f64 (Rewrite=> unpow2_binary64 (*.f64 B B)) (pow.f64 C 2)))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 0 points increase in error, 19 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (sqrt.f64 (+.f64 (*.f64 B B) (Rewrite=> unpow2_binary64 (*.f64 C C))))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 18 points increase in error, 1 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (Rewrite=> hypot-def_binary64 (hypot.f64 B C))))) (/.f64 (*.f64 B (sqrt.f64 F)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 6 points increase in error, 13 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 B (sqrt.f64 F)) 1)) (fma.f64 B B (*.f64 (*.f64 -4 C) A)))): 0 points increase in error, 13 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (/.f64 (*.f64 (*.f64 B (sqrt.f64 F)) 1) (fma.f64 B B (Rewrite<= associate-*r*_binary64 (*.f64 -4 (*.f64 C A)))))): 13 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (/.f64 (*.f64 (*.f64 B (sqrt.f64 F)) 1) (fma.f64 B B (*.f64 -4 (Rewrite<= *-commutative_binary64 (*.f64 A C)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (/.f64 (*.f64 (*.f64 B (sqrt.f64 F)) 1) (fma.f64 B B (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 A C) -4))))): 0 points increase in error, 19 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (/.f64 (*.f64 (*.f64 B (sqrt.f64 F)) 1) (fma.f64 B B (*.f64 (Rewrite=> *-commutative_binary64 (*.f64 C A)) -4)))): 2 points increase in error, 17 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 B (sqrt.f64 F)) (/.f64 1 (fma.f64 B B (*.f64 (*.f64 C A) -4)))))): 17 points increase in error, 2 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (*.f64 B (sqrt.f64 F))) (/.f64 1 (fma.f64 B B (*.f64 (*.f64 C A) -4))))): 13 points increase in error, 6 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (*.f64 B (sqrt.f64 F))) 1) (fma.f64 B B (*.f64 (*.f64 C A) -4)))): 19 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> *-rgt-identity_binary64 (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (*.f64 B (sqrt.f64 F)))) (fma.f64 B B (*.f64 (*.f64 C A) -4))): 0 points increase in error, 19 points decrease in error
      (Rewrite<= expm1-log1p_binary64 (expm1.f64 (log1p.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (*.f64 B (sqrt.f64 F))) (fma.f64 B B (*.f64 (*.f64 C A) -4)))))): 18 points increase in error, 1 points decrease in error
      (Rewrite<= expm1-def_binary64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 B C)))) (*.f64 B (sqrt.f64 F))) (fma.f64 B B (*.f64 (*.f64 C A) -4))))) 1)): 19 points increase in error, 0 points decrease in error

   7. Taylor expanded in B around inf 23.7

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

   8. Simplified 23.7

      \[\leadsto \sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \color{blue}{\frac{\sqrt{F}}{B}} \]
      Proof
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 C B)))) (/.f64 (sqrt.f64 F) B)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 C B)))) (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (sqrt.f64 F) 1)) B)): 3 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 2 (+.f64 C (hypot.f64 C B)))) (Rewrite<= associate-*r/_binary64 (*.f64 (sqrt.f64 F) (/.f64 1 B)))): 3 points increase in error, 0 points decrease in error

   if -6.4999999999999999e98 < B < 2.5000000000000001e-251 or 8.2e-184 < B < 2.0499999999999999e99

   1. Initial program 48.0

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

   2. Simplified 48.0

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 37.8

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

   4. Simplified 37.8

      \[\leadsto \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right) \cdot F}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C)))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C)))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2))))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (Rewrite<= *-commutative_binary64 (*.f64 F (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error

   if 2.5000000000000001e-251 < B < 8.2e-184

   1. Initial program 52.9

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

   2. Simplified 47.8

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in A around -inf 49.4

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

   if 2.0499999999999999e99 < B

   1. Initial program 61.0

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

   2. Simplified 61.0

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (pow.f64 (-.f64 A C) 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (+.f64 (+.f64 A C) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in A around 0 57.8

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

   4. Simplified 57.8

      \[\leadsto \frac{-\color{blue}{\sqrt{F \cdot \left(C + \sqrt{B \cdot B + C \cdot C}\right)} \cdot \left(B \cdot \sqrt{2}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C)))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C)))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2))))) (*.f64 (*.f64 B B) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) F))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 0 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (Rewrite<= *-commutative_binary64 (*.f64 F (pow.f64 B 2))))))) (-.f64 (*.f64 B B) (*.f64 4 (*.f64 A C)))): 5 points increase in error, 0 points decrease in error

   5. Taylor expanded in C around 0 32.5

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

   6. Simplified 32.5

      \[\leadsto \color{blue}{\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)} \]
      Proof
      (*.f64 (sqrt.f64 (/.f64 F B)) (neg.f64 (sqrt.f64 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 (/.f64 F B)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (sqrt.f64 2))) (sqrt.f64 (/.f64 F B))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 F B))))): 0 points increase in error, 0 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 35.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{+98}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-184}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{F \cdot \left(2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	35.0
Cost	34120

\[\begin{array}{l} t_0 := \mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{+98}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{+101}:\\ \;\;\;\;\frac{\sqrt{C + \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}}{t_0} \cdot \left(-\sqrt{2 \cdot \left(F \cdot t_0\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 2
Error	37.3
Cost	27724

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \mathsf{fma}\left(B, B, t_0\right)\\ t_2 := \sqrt{C + \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}\\ \mathbf{if}\;B \leq -0.00015:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-164}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-148}:\\ \;\;\;\;\frac{\left(-t_2\right) \cdot \sqrt{2 \cdot \left(F \cdot t_1\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{t_2}{\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)} \cdot \left(B \cdot \left(-\sqrt{2 \cdot F}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 3
Error	37.9
Cost	27592

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \sqrt{C + \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}\\ \mathbf{if}\;B \leq -5.8 \cdot 10^{-20}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-148}:\\ \;\;\;\;\frac{\left(-t_1\right) \cdot \sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_0\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{t_1}{\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)} \cdot \left(B \cdot \left(-\sqrt{2 \cdot F}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 4
Error	38.9
Cost	27468

\[\begin{array}{l} t_0 := \sqrt{C + \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}\\ \mathbf{if}\;B \leq -5.5 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-148}:\\ \;\;\;\;-\frac{t_0 \cdot \sqrt{\left(\left(C \cdot F\right) \cdot \left(A \cdot 4\right)\right) \cdot -2}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{t_0}{\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right)} \cdot \left(B \cdot \left(-\sqrt{2 \cdot F}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 5
Error	39.5
Cost	27212

\[\begin{array}{l} t_0 := \sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ \mathbf{if}\;B \leq -7.8 \cdot 10^{-144}:\\ \;\;\;\;t_0 \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;-\frac{\sqrt{C + \left(A + \mathsf{hypot}\left(A - C, B\right)\right)} \cdot \sqrt{\left(\left(C \cdot F\right) \cdot \left(A \cdot 4\right)\right) \cdot -2}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{t_0}{\frac{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}{B \cdot \left(-\sqrt{F}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 6
Error	41.3
Cost	21204

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ t_1 := \sqrt{\frac{-F}{C}}\\ t_2 := \sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ \mathbf{if}\;B \leq -1.5 \cdot 10^{-135}:\\ \;\;\;\;t_2 \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{C \cdot \left(A \cdot -4\right) + {B}^{2}}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{+90}:\\ \;\;\;\;\frac{B \cdot \left(t_2 \cdot \left(-\sqrt{F}\right)\right)}{t_0}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 7
Error	39.6
Cost	21064

\[\begin{array}{l} t_0 := \sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ \mathbf{if}\;B \leq -8.4 \cdot 10^{-141}:\\ \;\;\;\;t_0 \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-148}:\\ \;\;\;\;-\frac{\sqrt{C + \left(A + \mathsf{hypot}\left(A - C, B\right)\right)} \cdot \sqrt{\left(\left(C \cdot F\right) \cdot \left(A \cdot 4\right)\right) \cdot -2}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{B \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 8
Error	40.8
Cost	20940

\[\begin{array}{l} t_0 := \sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ t_1 := C \cdot \left(A \cdot -4\right)\\ \mathbf{if}\;B \leq -6.6 \cdot 10^{-20}:\\ \;\;\;\;t_0 \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 1.08 \cdot 10^{-159}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)} \cdot \left(-\sqrt{C + C}\right)}{t_1}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{B \cdot \left(t_0 \cdot \left(-\sqrt{F}\right)\right)}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 9
Error	42.0
Cost	20828

\[\begin{array}{l} t_0 := \sqrt{\frac{-F}{C}}\\ t_1 := \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(A + \mathsf{hypot}\left(B, A\right)\right)}\right)\\ \mathbf{if}\;B \leq -8.2 \cdot 10^{-133}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-240}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{C \cdot \left(A \cdot -4\right) + {B}^{2}}\\ \mathbf{elif}\;B \leq 0.0036:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 0.72:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 10
Error	41.8
Cost	20432

\[\begin{array}{l} t_0 := -\sqrt{2}\\ t_1 := C + \mathsf{hypot}\left(C, B\right)\\ \mathbf{if}\;B \leq -1.5 \cdot 10^{-139}:\\ \;\;\;\;\sqrt{2 \cdot t_1} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{C \cdot \left(A \cdot -4\right) + {B}^{2}}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;\sqrt{t_1 \cdot F} \cdot \frac{t_0}{B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot t_0\\ \end{array} \]

Alternative 11
Error	42.2
Cost	19972

\[\begin{array}{l} \mathbf{if}\;B \leq -2.85 \cdot 10^{-130}:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{\sqrt{F}}{B}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-180}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{C \cdot \left(A \cdot -4\right) + {B}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 12
Error	49.7
Cost	14412

\[\begin{array}{l} \mathbf{if}\;B \leq -0.0014:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C - B\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-241}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-170}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{C \cdot \left(A \cdot -4\right) + {B}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 13
Error	48.4
Cost	14412

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;-\frac{\sqrt{B \cdot \left(\left(C + \mathsf{hypot}\left(C, B\right)\right) \cdot \left(B \cdot \left(2 \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-253}:\\ \;\;\;\;-\frac{{\left(-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)\right)}^{0.5}}{t_0}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-170}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{C \cdot \left(A \cdot -4\right) + {B}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 14
Error	52.8
Cost	13980

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -1.28 \cdot 10^{-45}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -8\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -3.45 \cdot 10^{-307}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-169}:\\ \;\;\;\;-\sqrt{F \cdot \left(B \cdot \frac{\frac{2}{B}}{B}\right)}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(C \cdot \left(A \cdot A\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{+60}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 10^{+150}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{+197}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 15
Error	49.7
Cost	13580

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ \mathbf{if}\;B \leq -0.000165:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C - B\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.06 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-173}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -8\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 16
Error	52.4
Cost	9112

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -1.05 \cdot 10^{-50}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -8\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-308}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-160}:\\ \;\;\;\;-\sqrt{F \cdot \left(B \cdot \frac{\frac{2}{B}}{B}\right)}\\ \mathbf{elif}\;A \leq 5.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(C \cdot \left(A \cdot A\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 17
Error	53.6
Cost	8980

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ t_1 := \sqrt{\frac{-F}{C}}\\ \mathbf{if}\;A \leq -6 \cdot 10^{-48}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -8\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-189}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C - B\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{+61}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	54.4
Cost	8204

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(C \cdot A\right)\\ t_1 := \sqrt{\frac{-F}{C}}\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -8\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-189}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(C - B\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.85 \cdot 10^{+60}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	53.7
Cost	7940

\[\begin{array}{l} t_0 := \sqrt{\frac{-F}{C}}\\ \mathbf{if}\;A \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -8\right)\right)}}{B \cdot B + -4 \cdot \left(C \cdot A\right)}\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{-163}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-162}:\\ \;\;\;\;-\sqrt{F \cdot \left(B \cdot \frac{\frac{2}{B}}{B}\right)}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{+61}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 20
Error	53.5
Cost	7436

\[\begin{array}{l} t_0 := \sqrt{\frac{-F}{A}}\\ t_1 := \sqrt{\frac{-F}{C}}\\ \mathbf{if}\;A \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-165}:\\ \;\;\;\;-\sqrt{F \cdot \left(B \cdot \frac{\frac{2}{B}}{B}\right)}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	54.3
Cost	7053

\[\begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{-17} \lor \neg \left(A \leq 7.5 \cdot 10^{-243}\right) \land A \leq 4.9 \cdot 10^{+61}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 22
Error	57.0
Cost	6656

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

Alternative 23
Error	63.3
Cost	6592

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

Reproduce

herbie shell --seed 2022343 
(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))))