ABCF->ab-angle a

Average Accuracy: 18.8% → 45.1%

Time: 1.3min

Precision: binary64

Cost: 149516

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_3 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ t_4 := \frac{-\sqrt{\left(2 \cdot \left(t_3 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_3}\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{-214}:\\ \;\;\;\;\frac{\left(t_0 \cdot \sqrt{F}\right) \cdot \left(-\sqrt{2 \cdot t_2}\right)}{t_2}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \mathsf{fma}\left(2, A, -0.5 \cdot \frac{B \cdot B}{C}\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{t_0 \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\right)}{B \cdot B + t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

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 (sqrt (+ A (+ C (hypot B (- A C))))))
        (t_1 (* -4.0 (* A C)))
        (t_2 (fma B B (* C (* A -4.0))))
        (t_3 (- (pow B 2.0) (* (* 4.0 A) C)))
        (t_4
         (/
          (-
           (sqrt
            (*
             (* 2.0 (* t_3 F))
             (+ (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))))))
          t_3)))
   (if (<= t_4 -1e-214)
     (/ (* (* t_0 (sqrt F)) (- (sqrt (* 2.0 t_2)))) t_2)
     (if (<= t_4 0.0)
       (/
        (- (sqrt (* 2.0 (* t_2 (* F (fma 2.0 A (* -0.5 (/ (* B B) C))))))))
        t_2)
       (if (<= t_4 INFINITY)
         (/ (* t_0 (- (sqrt (* 2.0 (* F (fma B B t_1)))))) (+ (* B B) t_1))
         (* (sqrt 2.0) (- (sqrt (/ F 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 = sqrt((A + (C + hypot(B, (A - C)))));
	double t_1 = -4.0 * (A * C);
	double t_2 = fma(B, B, (C * (A * -4.0)));
	double t_3 = pow(B, 2.0) - ((4.0 * A) * C);
	double t_4 = -sqrt(((2.0 * (t_3 * F)) * ((A + C) + sqrt((pow(B, 2.0) + pow((A - C), 2.0)))))) / t_3;
	double tmp;
	if (t_4 <= -1e-214) {
		tmp = ((t_0 * sqrt(F)) * -sqrt((2.0 * t_2))) / t_2;
	} else if (t_4 <= 0.0) {
		tmp = -sqrt((2.0 * (t_2 * (F * fma(2.0, A, (-0.5 * ((B * B) / C))))))) / t_2;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (t_0 * -sqrt((2.0 * (F * fma(B, B, t_1))))) / ((B * B) + t_1);
	} else {
		tmp = sqrt(2.0) * -sqrt((F / 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 = sqrt(Float64(A + Float64(C + hypot(B, Float64(A - C)))))
	t_1 = Float64(-4.0 * Float64(A * C))
	t_2 = fma(B, B, Float64(C * Float64(A * -4.0)))
	t_3 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	t_4 = Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_3 * F)) * Float64(Float64(A + C) + sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0))))))) / t_3)
	tmp = 0.0
	if (t_4 <= -1e-214)
		tmp = Float64(Float64(Float64(t_0 * sqrt(F)) * Float64(-sqrt(Float64(2.0 * t_2)))) / t_2);
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_2 * Float64(F * fma(2.0, A, Float64(-0.5 * Float64(Float64(B * B) / C)))))))) / t_2);
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(t_0 * Float64(-sqrt(Float64(2.0 * Float64(F * fma(B, B, t_1)))))) / Float64(Float64(B * B) + t_1));
	else
		tmp = Float64(sqrt(2.0) * Float64(-sqrt(Float64(F / B))));
	end
	return tmp
end

Wolfram

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

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[Sqrt[N[(A + N[(C + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(A * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(B * B + N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$3 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, -1e-214], N[(N[(N[(t$95$0 * N[Sqrt[F], $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[N[(2.0 * t$95$2), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[((-N[Sqrt[N[(2.0 * N[(t$95$2 * N[(F * N[(2.0 * A + N[(-0.5 * N[(N[(B * B), $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$2), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(t$95$0 * (-N[Sqrt[N[(2.0 * N[(F * N[(B * B + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / N[(N[(B * B), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[2.0], $MachinePrecision] * (-N[Sqrt[N[(F / B), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.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 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < -9.99999999999999913e-215

   1. Initial program 41.7%

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

   2. Simplified 50.6%

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

      [Start] 41.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 64.8%

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

      [Start] 50.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r* [=>] 50.7	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right) \cdot \left(F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-prod [=>] 65.7	\[ \frac{-\color{blue}{\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+r+ [=>] 64.8	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{F \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 64.8	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{F \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 64.8	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{F \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \color{blue}{\left(C + A\right)}\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   4. Simplified 65.7%

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

      [Start] 64.8	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \sqrt{F \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 64.8	\[ \frac{-\color{blue}{\sqrt{F \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+r+ [=>] 65.7	\[ \frac{-\sqrt{F \cdot \color{blue}{\left(\left(\mathsf{hypot}\left(B, A - C\right) + C\right) + A\right)}} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [<=] 65.7	\[ \frac{-\sqrt{F \cdot \left(\color{blue}{\left(C + \mathsf{hypot}\left(B, A - C\right)\right)} + A\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [<=] 65.7	\[ \frac{-\sqrt{F \cdot \color{blue}{\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   5. Applied egg-rr 75.5%

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

      [Start] 65.7	\[ \frac{-\sqrt{F \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      sqrt-prod [=>] 75.6	\[ \frac{-\color{blue}{\left(\sqrt{F} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      *-commutative [=>] 75.6	\[ \frac{-\color{blue}{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{F}\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 75.6	\[ \frac{-\left(\sqrt{A + \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + C\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+r+ [=>] 75.5	\[ \frac{-\left(\sqrt{\color{blue}{\left(A + \mathsf{hypot}\left(B, A - C\right)\right) + C}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [<=] 75.5	\[ \frac{-\left(\sqrt{\color{blue}{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   6. Applied egg-rr 61.2%

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

      [Start] 75.5	\[ \frac{-\left(\sqrt{C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      expm1-log1p-u [=>] 71.5	\[ \frac{-\left(\sqrt{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      expm1-udef [=>] 61.2	\[ \frac{-\left(\sqrt{\color{blue}{e^{\mathsf{log1p}\left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} - 1}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 61.2	\[ \frac{-\left(\sqrt{e^{\mathsf{log1p}\left(C + \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + A\right)}\right)} - 1} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-+r+ [=>] 61.2	\[ \frac{-\left(\sqrt{e^{\mathsf{log1p}\left(\color{blue}{\left(C + \mathsf{hypot}\left(B, A - C\right)\right) + A}\right)} - 1} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      +-commutative [=>] 61.2	\[ \frac{-\left(\sqrt{e^{\mathsf{log1p}\left(\color{blue}{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\right)} - 1} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   7. Simplified 75.6%

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

      [Start] 61.2	\[ \frac{-\left(\sqrt{e^{\mathsf{log1p}\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)} - 1} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      expm1-def [=>] 71.6	\[ \frac{-\left(\sqrt{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      expm1-log1p [=>] 75.6	\[ \frac{-\left(\sqrt{\color{blue}{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{F}\right) \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   if -9.99999999999999913e-215 < (/.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 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < -0.0

   1. Initial program 4.1%

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

   2. Simplified 9.6%

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

      [Start] 4.1	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in C around -inf 28.9%

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

   4. Simplified 28.9%

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

      [Start] 28.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(2 \cdot A + -0.5 \cdot \frac{{B}^{2}}{C}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      fma-def [=>] 28.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \color{blue}{\mathsf{fma}\left(2, A, -0.5 \cdot \frac{{B}^{2}}{C}\right)}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 28.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, A, -0.5 \cdot \frac{\color{blue}{B \cdot B}}{C}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   if -0.0 < (/.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 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < +inf.0

   1. Initial program 41.2%

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

   2. Simplified 41.2%

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

      [Start] 41.2	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 81.9%

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

      [Start] 41.2	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-*r* [=>] 41.2	\[ \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      sqrt-prod [=>] 43.6	\[ \frac{-\color{blue}{\sqrt{2 \cdot \left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      fma-neg [=>] 43.6	\[ \frac{-\sqrt{2 \cdot \left(\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)} \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      distribute-lft-neg-in [=>] 43.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(-4\right) \cdot \left(A \cdot C\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 43.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \color{blue}{\left(A \cdot C\right) \cdot \left(-4\right)}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      metadata-eval [=>] 43.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot \color{blue}{-4}\right) \cdot F\right)} \cdot \sqrt{\left(A + C\right) + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      associate-+l+ [=>] 43.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{\color{blue}{A + \left(C + \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 43.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      hypot-def [=>] 81.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   4. Simplified 81.9%

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

      [Start] 81.9	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)} \cdot \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 81.9	\[ \frac{-\color{blue}{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right) \cdot F\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 81.9	\[ \frac{-\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{2 \cdot \color{blue}{\left(F \cdot \mathsf{fma}\left(B, B, \left(A \cdot C\right) \cdot -4\right)\right)}}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   if +inf.0 < (/.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 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))

   1. Initial program 0.0%

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

   2. Simplified 0.0%

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

      [Start] 0.0	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around 0 0.4%

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

   4. Simplified 0.4%

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

      [Start] 0.4	\[ \frac{-\sqrt{\left(C + \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 0.4	\[ \frac{-\sqrt{\color{blue}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 0.4	\[ \frac{-\sqrt{F \cdot \left(C + \sqrt{\color{blue}{B \cdot B} + {C}^{2}}\right)} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 0.4	\[ \frac{-\sqrt{F \cdot \left(C + \sqrt{B \cdot B + \color{blue}{C \cdot C}}\right)} \cdot \left(\sqrt{2} \cdot B\right)}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      *-commutative [=>] 0.4	\[ \frac{-\sqrt{F \cdot \left(C + \sqrt{B \cdot B + C \cdot C}\right)} \cdot \color{blue}{\left(B \cdot \sqrt{2}\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in C around 0 17.3%

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

   6. Simplified 17.3%

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

      [Start] 17.3	\[ -1 \cdot \left(\sqrt{2} \cdot \sqrt{\frac{F}{B}}\right) \]
      mul-1-neg [=>] 17.3	\[ \color{blue}{-\sqrt{2} \cdot \sqrt{\frac{F}{B}}} \]
      distribute-rgt-neg-in [=>] 17.3	\[ \color{blue}{\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq -1 \cdot 10^{-214}:\\ \;\;\;\;\frac{\left(\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{F}\right) \cdot \left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq 0:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, A, -0.5 \cdot \frac{B \cdot B}{C}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq \infty:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)\right)}\right)}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	37.7%
Cost	33540

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := -4 \cdot \left(A \cdot C\right)\\ t_3 := \frac{\sqrt{A + \left(C + t_0\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_2\right)\right)}\right)}{B \cdot B + t_2}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+60}:\\ \;\;\;\;\frac{\left(\sqrt{F} \cdot \sqrt{C + \left(A + t_0\right)}\right) \cdot \left(B \cdot \sqrt{2}\right)}{t_1}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-192}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right) \cdot \left(\left(C \cdot F\right) \cdot -2\right)\right|}}{t_1}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-223}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \mathsf{fma}\left(2, A, -0.5 \cdot \frac{B \cdot B}{C}\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 2
Accuracy	33.3%
Cost	28248

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_2 := \sqrt{t_1}\\ t_3 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_4 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ \mathbf{if}\;B \leq -7 \cdot 10^{-22}:\\ \;\;\;\;\frac{t_2 \cdot \left(\sqrt{2} \cdot \left(B \cdot \sqrt{F}\right)\right)}{t_0}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right) \cdot \left(\left(C \cdot F\right) \cdot -2\right)\right|}}{t_3}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_0}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot t_4\right) \cdot \left(2 \cdot t_1\right)}}{t_4}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 3
Accuracy	33.4%
Cost	28248

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\\ t_4 := \sqrt{t_3}\\ \mathbf{if}\;B \leq -2.7 \cdot 10^{-31}:\\ \;\;\;\;\frac{t_4 \cdot \left(\sqrt{2} \cdot \left(B \cdot \sqrt{F}\right)\right)}{t_2}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-147}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right) \cdot \left(\left(C \cdot F\right) \cdot -2\right)\right|}}{t_0}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-224}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \mathsf{fma}\left(2, A, -0.5 \cdot \frac{B \cdot B}{C}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-105}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot t_1\right) \cdot \left(2 \cdot t_3\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 4
Accuracy	37.7%
Cost	28244

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := B \cdot B + t_1\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_4 := \frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\right)}{t_2}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{+60}:\\ \;\;\;\;\frac{t_3 \cdot \left(\sqrt{2} \cdot \left(B \cdot \sqrt{F}\right)\right)}{t_2}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-215}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right) \cdot \left(\left(C \cdot F\right) \cdot -2\right)\right|}}{t_0}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-224}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \mathsf{fma}\left(2, A, -0.5 \cdot \frac{B \cdot B}{C}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{+107}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 5
Accuracy	31.6%
Cost	27736

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := A \cdot \left(C \cdot -4\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := B \cdot \sqrt{2}\\ t_4 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-31}:\\ \;\;\;\;t_3 \cdot \frac{\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-147}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{+153}:\\ \;\;\;\;\frac{t_3 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{C + \mathsf{hypot}\left(C, B\right)}\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 6
Accuracy	31.3%
Cost	27736

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := C + \mathsf{hypot}\left(C, B\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := B \cdot \sqrt{2}\\ t_4 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;t_3 \cdot \frac{\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-198}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right) \cdot \left(\left(C \cdot F\right) \cdot -2\right)\right|}}{t_0}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{+153}:\\ \;\;\;\;\frac{t_3 \cdot \left(\sqrt{F} \cdot \left(-\sqrt{t_1}\right)\right)}{t_2}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{+259}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot t_1} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 7
Accuracy	32.9%
Cost	27736

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := C + \mathsf{hypot}\left(C, B\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -9.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{t_3 \cdot \left(\sqrt{2} \cdot \left(B \cdot \sqrt{F}\right)\right)}{t_2}\\ \mathbf{elif}\;B \leq -2.65 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-204}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left|\mathsf{fma}\left(C, A \cdot -4, B \cdot B\right) \cdot \left(\left(C \cdot F\right) \cdot -2\right)\right|}}{t_0}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;\frac{\left(B \cdot \sqrt{2}\right) \cdot \left(\sqrt{F} \cdot \left(-\sqrt{t_1}\right)\right)}{t_2}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{+256}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot t_1} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 8
Accuracy	30.9%
Cost	26884

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := A \cdot \left(C \cdot -4\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -8 \cdot 10^{-31}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)} \cdot \frac{B}{\frac{t_0}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-198}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 9
Accuracy	30.7%
Cost	26884

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := A \cdot \left(C \cdot -4\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := \sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)}\\ t_4 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;t_3 \cdot \left(\sqrt{2} \cdot \frac{B}{t_0}\right)\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-194}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_4 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3 \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 10
Accuracy	30.7%
Cost	26884

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := A \cdot \left(C \cdot -4\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{-30}:\\ \;\;\;\;\left(B \cdot \sqrt{2}\right) \cdot \frac{\sqrt{F \cdot \left(C + \mathsf{hypot}\left(B, C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 11
Accuracy	29.7%
Cost	21716

\[\begin{array}{l} t_0 := A \cdot \left(C \cdot -4\right)\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ t_3 := \frac{t_2 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_1}\\ t_4 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -2.55 \cdot 10^{-28}:\\ \;\;\;\;\frac{t_2 \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_1}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-147}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-224}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_4 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{+26}:\\ \;\;\;\;\sqrt{t_4 \cdot \left(2 \cdot \left(A \cdot \left(2 \cdot F\right)\right)\right)} \cdot \frac{-1}{t_4}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 12
Accuracy	30.9%
Cost	21716

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_1 := A \cdot \left(C \cdot -4\right)\\ t_2 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_3 := \sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)}\\ \mathbf{if}\;B \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(C \cdot F\right)\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-201}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-223}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_0 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_3 \cdot \left(-\sqrt{2 \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 13
Accuracy	28.8%
Cost	21060

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \mathsf{fma}\left(B, B, t_0\right)\\ \mathbf{if}\;B \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot \left(B \cdot \left(B \cdot F\right)\right)}\right)}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-201}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 14
Accuracy	26.0%
Cost	21000

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := C \cdot \left(A \cdot -4\right)\\ t_2 := \mathsf{fma}\left(B, B, t_1\right)\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{-42}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-192}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 15
Accuracy	27.1%
Cost	21000

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \mathsf{fma}\left(B, B, t_0\right)\\ \mathbf{if}\;B \leq -1.16 \cdot 10^{-74}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \left(B \cdot \left(B \cdot F\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_0 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 16
Accuracy	25.7%
Cost	20300

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := C \cdot \left(A \cdot -4\right)\\ t_2 := \mathsf{fma}\left(B, B, t_1\right)\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-42}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-194}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C + \mathsf{hypot}\left(C, B\right)\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]

Alternative 17
Accuracy	25.4%
Cost	14860

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := C \cdot \left(A \cdot -4\right)\\ t_2 := \mathsf{fma}\left(B, B, t_1\right)\\ \mathbf{if}\;B \leq -1 \cdot 10^{-41}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-195}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_1 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 18
Accuracy	23.8%
Cost	14736

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ t_2 := F \cdot t_0\\ \mathbf{if}\;B \leq -3.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(t_2 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 19
Accuracy	25.0%
Cost	14604

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\\ t_2 := A \cdot \left(C \cdot -4\right)\\ \mathbf{if}\;B \leq -1.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{+26}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right)}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 20
Accuracy	22.5%
Cost	14216

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -8.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(t_1 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -16\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 21
Accuracy	22.5%
Cost	13580

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(t_1 \cdot \left(B - \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-260}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(-\sqrt{\frac{F}{B}}\right)\\ \end{array} \]

Alternative 22
Accuracy	17.4%
Cost	8712

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 2.65 \cdot 10^{-110}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A + C\right) + \left(A - C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 23
Accuracy	17.3%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 2.7 \cdot 10^{-110}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 24
Accuracy	12.8%
Cost	8452

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -7.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 25
Accuracy	11.6%
Cost	8196

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -1.82 \cdot 10^{-6}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(-4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 26
Accuracy	9.9%
Cost	7940

\[\begin{array}{l} \mathbf{if}\;C \leq 9.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\sqrt{C \cdot F} \cdot \frac{1}{B}\right)\\ \end{array} \]

Alternative 27
Accuracy	5.7%
Cost	7108

\[\begin{array}{l} \mathbf{if}\;C \leq 1.8 \cdot 10^{-156}:\\ \;\;\;\;-2 \cdot \sqrt{F \cdot \frac{A}{B \cdot B}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\sqrt{C \cdot F}}{B}\\ \end{array} \]

Alternative 28
Accuracy	5.7%
Cost	7108

\[\begin{array}{l} \mathbf{if}\;C \leq 3.9 \cdot 10^{-156}:\\ \;\;\;\;-2 \cdot \sqrt{F \cdot \frac{A}{B \cdot B}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\sqrt{C \cdot F} \cdot \frac{1}{B}\right)\\ \end{array} \]

Alternative 29
Accuracy	4.7%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;C \leq 8.5 \cdot 10^{-255}:\\ \;\;\;\;2 \cdot \frac{\sqrt{A \cdot F}}{B}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\sqrt{C \cdot F}}{B}\\ \end{array} \]

Alternative 30
Accuracy	2.9%
Cost	6848

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

Alternative 31
Accuracy	3.0%
Cost	6848

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

Reproduce

herbie shell --seed 2023130 
(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))))