ABCF->ab-angle a

Average Error: 81.61% → 57.86%

Time: 1.1min

Precision: binary64

Cost: 27848

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_2 := \left(C \cdot A\right) \cdot -4\\ t_3 := t_2 + B \cdot B\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_2\right)\right)} \cdot \left(-t_1\right)}{t_3}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+154}:\\ \;\;\;\;\frac{t_1 \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

FPCore

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

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (fma B B (* C (* A -4.0))))
        (t_1 (sqrt (+ A (+ C (hypot B (- A C))))))
        (t_2 (* (* C A) -4.0))
        (t_3 (+ t_2 (* B B))))
   (if (<= B -3.2e+88)
     (* (/ (sqrt 2.0) B) (* (sqrt (+ C (hypot B C))) (sqrt F)))
     (if (<= B 1.25e-82)
       (/ (* (sqrt (* 2.0 (* F (fma B B t_2)))) (- t_1)) t_3)
       (if (<= B 4.8e-32)
         (/
          (- (sqrt (* 2.0 (* t_0 (* F (+ A (+ A (/ (* (* B B) -0.5) C))))))))
          t_0)
         (if (<= B 6e+154)
           (/ (* t_1 (* (sqrt 2.0) (* (sqrt F) (- B)))) t_3)
           (* (sqrt (* F A)) (/ (- (pow (sqrt 2.0) 2.0)) B))))))))

C

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

↓

double code(double A, double B, double C, double F) {
	double t_0 = fma(B, B, (C * (A * -4.0)));
	double t_1 = sqrt((A + (C + hypot(B, (A - C)))));
	double t_2 = (C * A) * -4.0;
	double t_3 = t_2 + (B * B);
	double tmp;
	if (B <= -3.2e+88) {
		tmp = (sqrt(2.0) / B) * (sqrt((C + hypot(B, C))) * sqrt(F));
	} else if (B <= 1.25e-82) {
		tmp = (sqrt((2.0 * (F * fma(B, B, t_2)))) * -t_1) / t_3;
	} else if (B <= 4.8e-32) {
		tmp = -sqrt((2.0 * (t_0 * (F * (A + (A + (((B * B) * -0.5) / C))))))) / t_0;
	} else if (B <= 6e+154) {
		tmp = (t_1 * (sqrt(2.0) * (sqrt(F) * -B))) / t_3;
	} else {
		tmp = sqrt((F * A)) * (-pow(sqrt(2.0), 2.0) / B);
	}
	return tmp;
}

Julia

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

↓

function code(A, B, C, F)
	t_0 = fma(B, B, Float64(C * Float64(A * -4.0)))
	t_1 = sqrt(Float64(A + Float64(C + hypot(B, Float64(A - C)))))
	t_2 = Float64(Float64(C * A) * -4.0)
	t_3 = Float64(t_2 + Float64(B * B))
	tmp = 0.0
	if (B <= -3.2e+88)
		tmp = Float64(Float64(sqrt(2.0) / B) * Float64(sqrt(Float64(C + hypot(B, C))) * sqrt(F)));
	elseif (B <= 1.25e-82)
		tmp = Float64(Float64(sqrt(Float64(2.0 * Float64(F * fma(B, B, t_2)))) * Float64(-t_1)) / t_3);
	elseif (B <= 4.8e-32)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_0 * Float64(F * Float64(A + Float64(A + Float64(Float64(Float64(B * B) * -0.5) / C)))))))) / t_0);
	elseif (B <= 6e+154)
		tmp = Float64(Float64(t_1 * Float64(sqrt(2.0) * Float64(sqrt(F) * Float64(-B)))) / t_3);
	else
		tmp = Float64(sqrt(Float64(F * A)) * Float64(Float64(-(sqrt(2.0) ^ 2.0)) / B));
	end
	return tmp
end

Wolfram

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

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(B * B + N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(A + N[(C + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(C * A), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(B * B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.2e+88], N[(N[(N[Sqrt[2.0], $MachinePrecision] / B), $MachinePrecision] * N[(N[Sqrt[N[(C + N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[F], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.25e-82], N[(N[(N[Sqrt[N[(2.0 * N[(F * N[(B * B + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-t$95$1)), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[B, 4.8e-32], N[((-N[Sqrt[N[(2.0 * N[(t$95$0 * N[(F * N[(A + N[(A + N[(N[(N[(B * B), $MachinePrecision] * -0.5), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision], If[LessEqual[B, 6e+154], N[(N[(t$95$1 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * (-B)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], N[(N[Sqrt[N[(F * A), $MachinePrecision]], $MachinePrecision] * N[((-N[Power[N[Sqrt[2.0], $MachinePrecision], 2.0], $MachinePrecision]) / B), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3.1999999999999999e88

   1. Initial program 93.55

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

   2. Simplified 93.55

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

      [Start] 93.55	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 99.46

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

   4. Simplified 99.32

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

      [Start] 99.46	\[ \sqrt{\frac{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)\right)}{{\left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}^{2}}} \]
      associate-/l* [=>] 99.32	\[ \sqrt{\color{blue}{\frac{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}^{2}}{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}} \]
      *-commutative [=>] 99.32	\[ \sqrt{\frac{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}^{2}}{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}} \]

   5. Taylor expanded in A around 0 88.44

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

   6. Simplified 88.44

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

      [Start] 88.44	\[ \frac{\sqrt{2}}{B} \cdot \sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \]
      *-commutative [=>] 88.44	\[ \frac{\sqrt{2}}{B} \cdot \sqrt{\color{blue}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}} \]
      unpow2 [=>] 88.44	\[ \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{\color{blue}{B \cdot B} + {C}^{2}}\right)} \]
      unpow2 [=>] 88.44	\[ \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{B \cdot B + \color{blue}{C \cdot C}}\right)} \]

   7. Applied egg-rr 24.11

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

   if -3.1999999999999999e88 < B < 1.25e-82

   1. Initial program 76.87

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

   2. Simplified 76.88

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

      [Start] 76.87	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 61.33

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

   4. Simplified 61.33

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

      [Start] 61.33	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 61.33	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 61.33	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if 1.25e-82 < B < 4.8000000000000003e-32

   1. Initial program 72.91

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

   2. Simplified 65.41

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

      [Start] 72.91	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in C around -inf 80.6

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

   4. Simplified 80.6

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

      [Start] 80.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(A + -0.5 \cdot \frac{{B}^{2}}{C}\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r/ [=>] 80.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(A + \color{blue}{\frac{-0.5 \cdot {B}^{2}}{C}}\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 80.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(A + \frac{-0.5 \cdot \color{blue}{\left(B \cdot B\right)}}{C}\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   if 4.8000000000000003e-32 < B < 6.00000000000000052e154

   1. Initial program 72.09

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

   2. Simplified 72.09

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

      [Start] 72.09	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 54.26

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

   4. Simplified 54.26

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

      [Start] 54.26	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 54.26	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 54.26	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in B around inf 51.29

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

   6. Simplified 51.29

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

      [Start] 51.29	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\left(\sqrt{2} \cdot B\right) \cdot \sqrt{F}\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*l* [=>] 51.29	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \color{blue}{\left(\sqrt{2} \cdot \left(B \cdot \sqrt{F}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if 6.00000000000000052e154 < B

   1. Initial program 100

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

   2. Simplified 100

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

      [Start] 100	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around inf 100

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

   4. Taylor expanded in C around 0 94.04

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

   5. Simplified 94.04

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

      [Start] 94.04	\[ -1 \cdot \left(\frac{{\left(\sqrt{2}\right)}^{2}}{B} \cdot \sqrt{A \cdot F}\right) \]
      mul-1-neg [=>] 94.04	\[ \color{blue}{-\frac{{\left(\sqrt{2}\right)}^{2}}{B} \cdot \sqrt{A \cdot F}} \]
      *-commutative [=>] 94.04	\[ -\color{blue}{\sqrt{A \cdot F} \cdot \frac{{\left(\sqrt{2}\right)}^{2}}{B}} \]

3. Recombined 5 regimes into one program.

4. Final simplification 57.86

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, \left(C \cdot A\right) \cdot -4\right)\right)} \cdot \left(-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}{\left(C \cdot A\right) \cdot -4 + B \cdot B}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{\left(C \cdot A\right) \cdot -4 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternatives

Alternative 1
Error	61.99%
Cost	27993

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4\\ t_1 := t_0 + B \cdot B\\ t_2 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_3 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-58}:\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{F} \cdot \left(B \cdot \sqrt{2}\right)\right)}{t_1}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-83} \lor \neg \left(B \leq 6.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_3}\\ \end{array} \]

Alternative 2
Error	62.11%
Cost	27993

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ t_2 := \sqrt{A + \left(C + t_1\right)}\\ t_3 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{F} \cdot \left(B \cdot \sqrt{2}\right)\right)}{t_0}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-223}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{\sqrt{C + \left(A + t_1\right)} \cdot \left(-\sqrt{F \cdot \left(A \cdot \left(2 \cdot \left(C \cdot -4\right)\right)\right)}\right)}{\mathsf{fma}\left(-4, C \cdot A, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-83} \lor \neg \left(B \leq 6.3 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_3}\\ \end{array} \]

Alternative 3
Error	64.01%
Cost	27992

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_3 := \frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ t_4 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot t_0\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-246}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-83}:\\ \;\;\;\;t_4 \cdot \frac{-\sqrt{\left(F \cdot \left(C \cdot A\right)\right) \cdot -8}}{t_0}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_4 \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{t_2}\\ \end{array} \]

Alternative 4
Error	62.39%
Cost	27984

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_2 := \sqrt{t_1}\\ t_3 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{+140}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq -9.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{F} \cdot \left(B \cdot \sqrt{2}\right)\right)}{t_0}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-257}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-39}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot t_1\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{t_0}\\ \end{array} \]

Alternative 5
Error	65.16%
Cost	27860

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_3 := \frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ t_4 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-31}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot t_0\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -2.65 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-244}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;t_4 \cdot \frac{-\sqrt{\left(F \cdot \left(C \cdot A\right)\right) \cdot -8}}{t_0}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{+155}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternative 6
Error	61.89%
Cost	27860

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.46 \cdot 10^{+137}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-58}:\\ \;\;\;\;\frac{t_1 \cdot \left(\sqrt{2} \cdot \left(B \cdot \sqrt{F}\right)\right)}{t_0}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-243}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-82}:\\ \;\;\;\;t_1 \cdot \frac{-\sqrt{\left(F \cdot \left(C \cdot A\right)\right) \cdot -8}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 \cdot \left(\sqrt{2} \cdot \left(\sqrt{F} \cdot \left(-B\right)\right)\right)}{t_0}\\ \end{array} \]

Alternative 7
Error	65%
Cost	26636

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_2 := \frac{\sqrt{2}}{B} \cdot \left(\sqrt{C + \mathsf{hypot}\left(B, C\right)} \cdot \sqrt{F}\right)\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-32}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq -5.7 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+158}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternative 8
Error	69.7%
Cost	22040

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_2 := \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -2.2 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-222}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + \left(A + \frac{\left(B \cdot B\right) \cdot -0.5}{C}\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{+154}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternative 9
Error	69.92%
Cost	21852

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_0}\\ t_2 := \frac{\sqrt{2}}{B}\\ t_3 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_4 := \frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_3}\\ \mathbf{if}\;B \leq -5.2 \cdot 10^{+87}:\\ \;\;\;\;t_2 \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ \mathbf{elif}\;B \leq -3.05 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-54}:\\ \;\;\;\;t_2 \cdot \sqrt{F \cdot \frac{B \cdot \left(B \cdot -0.5\right)}{C}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-258}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternative 10
Error	71.27%
Cost	21852

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_2 := \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ t_3 := \frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-33}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq -2.15 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.52 \cdot 10^{-86}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_1\right) \cdot \left(\left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternative 11
Error	69.71%
Cost	21852

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_2 := \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_4 := \frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.55 \cdot 10^{-31}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + A\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -6.6 \cdot 10^{-225}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot A} \cdot \frac{-{\left(\sqrt{2}\right)}^{2}}{B}\\ \end{array} \]

Alternative 12
Error	70.82%
Cost	20868

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;C \leq -16000000:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(A + A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;C \leq 6 \cdot 10^{+169}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \]

Alternative 13
Error	80.39%
Cost	15580

\[\begin{array}{l} t_0 := \left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\\ t_1 := \sqrt{-\frac{F}{C}}\\ t_2 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_3 := \frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(-4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)\right)}}{t_2}\\ t_4 := \frac{-\sqrt{2 \cdot \left(\left(B \cdot \left(B \cdot F\right)\right) \cdot t_0\right)}}{t_2}\\ \mathbf{if}\;C \leq -5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-236}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \left(\frac{C \cdot -0.5}{\frac{B}{C}} - B\right)\right)}\\ \mathbf{elif}\;C \leq 1.38 \cdot 10^{-160}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2 \cdot 10^{+102}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \]

Alternative 14
Error	73.62%
Cost	15448

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(-4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)\right)}}{t_0}\\ t_3 := \frac{\sqrt{2}}{B}\\ t_4 := B \cdot \left(B \cdot F\right)\\ t_5 := \frac{-\sqrt{2 \cdot \left(t_4 \cdot t_1\right)}}{t_0}\\ \mathbf{if}\;B \leq -1.25 \cdot 10^{+48}:\\ \;\;\;\;t_3 \cdot \sqrt{F \cdot \left(C - B\right)}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-37}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-51}:\\ \;\;\;\;t_3 \cdot \sqrt{F \cdot \frac{B \cdot \left(B \cdot -0.5\right)}{C}}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \mathsf{fma}\left(-8, F \cdot \left(A \cdot \left(C \cdot A\right)\right), A \cdot \left(4 \cdot t_4\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 15
Error	80.89%
Cost	15188

\[\begin{array}{l} t_0 := \sqrt{-\frac{F}{C}}\\ t_1 := \frac{-\sqrt{2 \cdot \left(\left(B \cdot \left(B \cdot F\right)\right) \cdot \left(\left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{\left(C \cdot A\right) \cdot -4 + B \cdot B}\\ \mathbf{if}\;C \leq -1.55 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{-236}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \left(\frac{C \cdot -0.5}{\frac{B}{C}} - B\right)\right)}\\ \mathbf{elif}\;C \leq 7.8 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 3.05 \cdot 10^{-46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \]

Alternative 16
Error	71.81%
Cost	15176

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ \mathbf{if}\;C \leq -1450000:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \mathsf{fma}\left(-8, F \cdot \left(A \cdot \left(C \cdot A\right)\right), A \cdot \left(4 \cdot \left(B \cdot \left(B \cdot F\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{+171}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(C + A\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \]

Alternative 17
Error	78.85%
Cost	14228

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \frac{\sqrt{2}}{B}\\ t_2 := F \cdot t_0\\ \mathbf{if}\;B \leq -6.4 \cdot 10^{+38}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(C - B\right)}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-245}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(C + A\right) + \left(\left(A - C\right) + 0.5 \cdot \frac{B \cdot B}{A}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-118}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(-\sqrt{F \cdot \left(C + 2 \cdot A\right)}\right)\\ \end{array} \]

Alternative 18
Error	79.56%
Cost	13508

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \mathbf{elif}\;B \leq 1.42 \cdot 10^{-245}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C + A\right) + \left(\left(A - C\right) + 0.5 \cdot \frac{B \cdot B}{A}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-41}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 19
Error	81.03%
Cost	13452

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -80:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C + A\right) + \left(\left(A - C\right) + 0.5 \cdot \frac{B \cdot B}{A}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{+170}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{-F}}{\sqrt{A}}\\ \end{array} \]

Alternative 20
Error	83.84%
Cost	9884

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := F \cdot t_0\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -3.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-124}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -4.5 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -5.2 \cdot 10^{-147}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-127}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C + A\right) + \left(\left(A - C\right) + 0.5 \cdot \frac{B \cdot B}{A}\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 21
Error	83.25%
Cost	9376

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ t_2 := F \cdot t_0\\ t_3 := \frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -1.12 \cdot 10^{+76}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -4.8 \cdot 10^{-141}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq -5.2 \cdot 10^{-151}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -6.9 \cdot 10^{-177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 22
Error	84.15%
Cost	9372

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := F \cdot t_0\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -6.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -1.25 \cdot 10^{-123}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -4.3 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -1.05 \cdot 10^{-156}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-124}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A - C\right) + \left(C + A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 23
Error	83.85%
Cost	9372

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := F \cdot t_0\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -3.55 \cdot 10^{-122}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-157}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-184}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(C + A\right) + \left(C - A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A - C\right) + \left(C + A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 24
Error	83.76%
Cost	9244

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := F \cdot t_0\\ t_2 := \frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ t_3 := \frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -3.5 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq -1.42 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{-221}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(B + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{-301}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{+119}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 25
Error	82.66%
Cost	8848

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ t_1 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;C \leq -10.5:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 5.8 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 26
Error	83.43%
Cost	8328

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ \mathbf{if}\;C \leq -255000:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;C \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + 2 \cdot A\right)\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+139}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 27
Error	83.13%
Cost	8328

\[\begin{array}{l} t_0 := \left(C \cdot A\right) \cdot -4 + B \cdot B\\ \mathbf{if}\;C \leq -860000:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(A + \left(C + A\right)\right) \cdot \left(4 \cdot \left(F \cdot \left(C \cdot A\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 1.3 \cdot 10^{+140}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 28
Error	86.65%
Cost	8073

\[\begin{array}{l} \mathbf{if}\;F \leq 1.08 \cdot 10^{-306} \lor \neg \left(F \leq 1.6 \cdot 10^{+76}\right):\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(A \cdot A\right) \cdot \left(C \cdot F\right)\right)\right)}}{\left(C \cdot A\right) \cdot -4 + B \cdot B}\\ \end{array} \]

Alternative 29
Error	84.07%
Cost	8072

\[\begin{array}{l} \mathbf{if}\;C \leq 9.4 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{+141}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(F \cdot \left(A \cdot \left(C \cdot C\right)\right)\right)\right)}}{\left(C \cdot A\right) \cdot -4 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 30
Error	84.45%
Cost	8072

\[\begin{array}{l} \mathbf{if}\;C \leq 4.4 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{elif}\;C \leq 2.85 \cdot 10^{+138}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A \cdot -8\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)}}{\left(C \cdot A\right) \cdot -4 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 31
Error	86.28%
Cost	6788

\[\begin{array}{l} \mathbf{if}\;C \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\sqrt{-\frac{F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-\frac{F}{A}}\\ \end{array} \]

Alternative 32
Error	89.01%
Cost	6656

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

Alternative 33
Error	98.84%
Cost	6592

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

Reproduce

herbie shell --seed 2023115 
(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))))