ABCF->ab-angle a

Average Accuracy: 18.4% → 50.1%

Time: 1.1min

Precision: binary64

Cost: 148940

Math

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

↓

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := \mathsf{fma}\left(B, B, t_0\right)\\ t_2 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_3 := {B}^{2} + t_0\\ t_4 := -\frac{\sqrt{\left(2 \cdot \left(t_3 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{t_3}\\ t_5 := \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ \mathbf{if}\;t_4 \leq -2 \cdot 10^{-196}:\\ \;\;\;\;\frac{t_5}{t_2} \cdot \left(\sqrt{t_2} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{\left(B \cdot B\right) \cdot -0.5}{A}\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5 \cdot \sqrt{F \cdot \frac{1}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (* C (* A -4.0)))
        (t_1 (fma B B t_0))
        (t_2 (fma -4.0 (* A C) (* B B)))
        (t_3 (+ (pow B 2.0) t_0))
        (t_4
         (-
          (/
           (sqrt
            (*
             (* 2.0 (* t_3 F))
             (+ (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0))))))
           t_3)))
        (t_5 (sqrt (* 2.0 (+ C (+ A (hypot B (- A C))))))))
   (if (<= t_4 -2e-196)
     (* (/ t_5 t_2) (* (sqrt t_2) (- (sqrt F))))
     (if (<= t_4 0.0)
       (/
        (- (sqrt (* 2.0 (* t_1 (* F (fma 2.0 C (/ (* (* B B) -0.5) A)))))))
        t_1)
       (if (<= t_4 INFINITY)
         (* t_5 (sqrt (* F (/ 1.0 (fma B B (* -4.0 (* A C)))))))
         (* (/ (- (sqrt 2.0)) B) (* (sqrt F) (sqrt (+ A (hypot B A))))))))))

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 = C * (A * -4.0);
	double t_1 = fma(B, B, t_0);
	double t_2 = fma(-4.0, (A * C), (B * B));
	double t_3 = pow(B, 2.0) + t_0;
	double t_4 = -(sqrt(((2.0 * (t_3 * F)) * ((A + C) + sqrt((pow(B, 2.0) + pow((A - C), 2.0)))))) / t_3);
	double t_5 = sqrt((2.0 * (C + (A + hypot(B, (A - C))))));
	double tmp;
	if (t_4 <= -2e-196) {
		tmp = (t_5 / t_2) * (sqrt(t_2) * -sqrt(F));
	} else if (t_4 <= 0.0) {
		tmp = -sqrt((2.0 * (t_1 * (F * fma(2.0, C, (((B * B) * -0.5) / A)))))) / t_1;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5 * sqrt((F * (1.0 / fma(B, B, (-4.0 * (A * C))))));
	} else {
		tmp = (-sqrt(2.0) / B) * (sqrt(F) * sqrt((A + hypot(B, A))));
	}
	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 = Float64(C * Float64(A * -4.0))
	t_1 = fma(B, B, t_0)
	t_2 = fma(-4.0, Float64(A * C), Float64(B * B))
	t_3 = Float64((B ^ 2.0) + t_0)
	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))
	t_5 = sqrt(Float64(2.0 * Float64(C + Float64(A + hypot(B, Float64(A - C))))))
	tmp = 0.0
	if (t_4 <= -2e-196)
		tmp = Float64(Float64(t_5 / t_2) * Float64(sqrt(t_2) * Float64(-sqrt(F))));
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_1 * Float64(F * fma(2.0, C, Float64(Float64(Float64(B * B) * -0.5) / A))))))) / t_1);
	elseif (t_4 <= Inf)
		tmp = Float64(t_5 * sqrt(Float64(F * Float64(1.0 / fma(B, B, Float64(-4.0 * Float64(A * C)))))));
	else
		tmp = Float64(Float64(Float64(-sqrt(2.0)) / B) * Float64(sqrt(F) * sqrt(Float64(A + hypot(B, A)))));
	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[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(B * B + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(A * C), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Power[B, 2.0], $MachinePrecision] + t$95$0), $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])}, Block[{t$95$5 = N[Sqrt[N[(2.0 * N[(C + N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$4, -2e-196], N[(N[(t$95$5 / t$95$2), $MachinePrecision] * N[(N[Sqrt[t$95$2], $MachinePrecision] * (-N[Sqrt[F], $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[((-N[Sqrt[N[(2.0 * N[(t$95$1 * N[(F * N[(2.0 * C + N[(N[(N[(B * B), $MachinePrecision] * -0.5), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(t$95$5 * N[Sqrt[N[(F * N[(1.0 / N[(B * B + N[(-4.0 * N[(A * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[((-N[Sqrt[2.0], $MachinePrecision]) / B), $MachinePrecision] * N[(N[Sqrt[F], $MachinePrecision] * N[Sqrt[N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]], $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))) < -2.0000000000000001e-196

   1. Initial program 40.7%

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

   2. Simplified 50.0%

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

      [Start] 40.7	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 63.3%

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

      [Start] 50.0	\[ \frac{-\sqrt{\left(\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F\right) \cdot \left(2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 64.1	\[ \frac{-\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      associate-+r+ [=>] 63.3	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 63.3	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   4. Applied egg-rr 64.0%

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

      [Start] 63.3	\[ \frac{-\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      distribute-rgt-neg-in [=>] 63.3	\[ \frac{\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \left(-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      *-un-lft-identity [=>] 63.3	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F} \cdot \left(-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}\right)}{\color{blue}{1 \cdot \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      times-frac [=>] 63.3	\[ \color{blue}{\frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(A + C\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}} \]
      associate-+r+ [=>] 64.0	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(\left(\mathsf{hypot}\left(B, A - C\right) + A\right) + C\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 64.0	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \color{blue}{\left(C + \left(\mathsf{hypot}\left(B, A - C\right) + A\right)\right)}}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      +-commutative [=>] 64.0	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \color{blue}{\left(A + \mathsf{hypot}\left(B, A - C\right)\right)}\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   5. Applied egg-rr 80.7%

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

      [Start] 64.0	\[ \frac{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right) \cdot F}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]
      sqrt-prod [=>] 80.7	\[ \frac{\color{blue}{\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \sqrt{F}}}{1} \cdot \frac{-\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \]

   if -2.0000000000000001e-196 < (/.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 6.3%

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

   2. Simplified 7.9%

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

      [Start] 6.3	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in A around -inf 29.7%

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

   4. Simplified 29.7%

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

      [Start] 29.7	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(2 \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      fma-def [=>] 29.7	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \color{blue}{\mathsf{fma}\left(2, C, -0.5 \cdot \frac{{B}^{2}}{A}\right)}\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      associate-*r/ [=>] 29.7	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, \color{blue}{\frac{-0.5 \cdot {B}^{2}}{A}}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      unpow2 [=>] 29.7	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{-0.5 \cdot \color{blue}{\left(B \cdot B\right)}}{A}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]

   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 39.4%

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

   2. Simplified 57.6%

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

      [Start] 39.4	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 37.5%

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

      [Start] 57.6	\[ \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \]
      add-sqr-sqrt [=>] 57.3	\[ \color{blue}{\sqrt{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}} \cdot \sqrt{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      sqrt-unprod [=>] 49.3	\[ \color{blue}{\sqrt{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)} \cdot \frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      frac-times [=>] 37.5	\[ \sqrt{\color{blue}{\frac{\left(-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}\right) \cdot \left(-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}\right)}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]

   4. Simplified 40.4%

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

      [Start] 37.5	\[ \sqrt{\frac{2 \cdot \left(\left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right)}{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}} \]
      associate-*r* [=>] 37.5	\[ \sqrt{\frac{\color{blue}{\left(2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot F\right)}}{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}} \]
      associate-/l* [=>] 40.4	\[ \sqrt{\color{blue}{\frac{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot F}}}} \]
      *-commutative [=>] 40.4	\[ \sqrt{\frac{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{\color{blue}{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}}} \]

   5. Applied egg-rr 45.9%

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

      [Start] 40.4	\[ \sqrt{\frac{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      div-inv [=>] 40.3	\[ \sqrt{\color{blue}{\left(2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)\right) \cdot \frac{1}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}}} \]
      sqrt-prod [=>] 47.0	\[ \color{blue}{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}}} \]
      associate-+r+ [=>] 47.0	\[ \sqrt{2 \cdot \color{blue}{\left(\left(C + A\right) + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      +-commutative [=>] 47.0	\[ \sqrt{2 \cdot \color{blue}{\left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}}} \]
      clear-num [<=] 47.3	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{\color{blue}{\frac{F \cdot \mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}}} \]
      *-commutative [=>] 47.3	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{\frac{\color{blue}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot F}}{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}} \]
      associate-/l* [=>] 45.9	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{\color{blue}{\frac{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F}}}} \]
      associate-*r* [=>] 45.9	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, \color{blue}{\left(C \cdot A\right) \cdot -4}\right)}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F}}} \]
      *-commutative [=>] 45.9	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, \color{blue}{-4 \cdot \left(C \cdot A\right)}\right)}{\frac{{\left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)\right)}^{2}}{F}}} \]

   6. Simplified 76.7%

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

      [Start] 45.9	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \left(C + A\right)\right)} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)\right)}^{2}}{F}}} \]
      +-commutative [<=] 45.9	\[ \sqrt{2 \cdot \left(\mathsf{hypot}\left(B, A - C\right) + \color{blue}{\left(A + C\right)}\right)} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)\right)}^{2}}{F}}} \]
      +-commutative [=>] 45.9	\[ \sqrt{2 \cdot \color{blue}{\left(\left(A + C\right) + \mathsf{hypot}\left(B, A - C\right)\right)}} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)\right)}^{2}}{F}}} \]
      +-commutative [=>] 45.9	\[ \sqrt{2 \cdot \left(\color{blue}{\left(C + A\right)} + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)\right)}^{2}}{F}}} \]
      associate-+l+ [=>] 45.9	\[ \sqrt{2 \cdot \color{blue}{\left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\frac{{\left(\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)\right)}^{2}}{F}}} \]
      associate-/r/ [=>] 52.7	\[ \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\color{blue}{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{{\left(\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)\right)}^{2}} \cdot F}} \]
      unpow2 [=>] 52.7	\[ \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\color{blue}{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right) \cdot \mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}} \cdot F} \]
      associate-/r* [=>] 76.7	\[ \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\color{blue}{\frac{\frac{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}}{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)}} \cdot F} \]
      *-inverses [=>] 76.7	\[ \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\frac{\color{blue}{1}}{\mathsf{fma}\left(B, B, -4 \cdot \left(C \cdot A\right)\right)} \cdot F} \]
      *-commutative [<=] 76.7	\[ \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{\frac{1}{\mathsf{fma}\left(B, B, -4 \cdot \color{blue}{\left(A \cdot C\right)}\right)} \cdot F} \]

   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 C around 0 0.5%

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

   4. Simplified 0.5%

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

      [Start] 0.5	\[ -1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}\right) \]
      associate-*r* [=>] 0.5	\[ \color{blue}{\left(-1 \cdot \frac{\sqrt{2}}{B}\right) \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F}} \]
      associate-*r/ [=>] 0.5	\[ \color{blue}{\frac{-1 \cdot \sqrt{2}}{B}} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F} \]
      mul-1-neg [=>] 0.5	\[ \frac{\color{blue}{-\sqrt{2}}}{B} \cdot \sqrt{\left(A + \sqrt{{B}^{2} + {A}^{2}}\right) \cdot F} \]
      *-commutative [=>] 0.5	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{\color{blue}{F \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}} \]
      unpow2 [=>] 0.5	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)} \]
      unpow2 [=>] 0.5	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)} \]

   5. Applied egg-rr 26.8%

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

      [Start] 0.5	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(A + \sqrt{B \cdot B + A \cdot A}\right)} \]
      sqrt-prod [=>] 0.5	\[ \frac{-\sqrt{2}}{B} \cdot \color{blue}{\left(\sqrt{F} \cdot \sqrt{A + \sqrt{B \cdot B + A \cdot A}}\right)} \]
      *-commutative [=>] 0.5	\[ \frac{-\sqrt{2}}{B} \cdot \color{blue}{\left(\sqrt{A + \sqrt{B \cdot B + A \cdot A}} \cdot \sqrt{F}\right)} \]
      hypot-def [=>] 26.8	\[ \frac{-\sqrt{2}}{B} \cdot \left(\sqrt{A + \color{blue}{\mathsf{hypot}\left(B, A\right)}} \cdot \sqrt{F}\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-\frac{\sqrt{\left(2 \cdot \left(\left({B}^{2} + C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq -2 \cdot 10^{-196}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \left(\sqrt{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)} \cdot \left(-\sqrt{F}\right)\right)\\ \mathbf{elif}\;-\frac{\sqrt{\left(2 \cdot \left(\left({B}^{2} + C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq 0:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right) \cdot \left(F \cdot \mathsf{fma}\left(2, C, \frac{\left(B \cdot B\right) \cdot -0.5}{A}\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;-\frac{\sqrt{\left(2 \cdot \left(\left({B}^{2} + C \cdot \left(A \cdot -4\right)\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq \infty:\\ \;\;\;\;\sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{F \cdot \frac{1}{\mathsf{fma}\left(B, B, -4 \cdot \left(A \cdot C\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	43.0%
Cost	34384

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{t_1}\\ t_3 := \sqrt{F \cdot t_1}\\ \mathbf{if}\;B \leq -4.6:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot t_2\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-161}:\\ \;\;\;\;\frac{t_3}{\frac{-t_1}{\sqrt{2 \cdot \left(A + \left(C + t_0\right)\right)}}}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-234}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;t_2 \cdot \left(-t_3\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 2
Accuracy	43.1%
Cost	34120

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \mathsf{hypot}\left(B, A - C\right)\\ t_3 := A + \left(C + t_2\right)\\ \mathbf{if}\;B \leq -4.6:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{\sqrt{2 \cdot \left(C + \left(A + t_2\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-160}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_0}}{\frac{-t_0}{\sqrt{2 \cdot t_3}}}\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-234}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{\sqrt{t_3} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\right)}{B \cdot B + t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 3
Accuracy	43.1%
Cost	28112

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \frac{\sqrt{A + \left(C + t_0\right)} \cdot \left(-\sqrt{2 \cdot \left(F \cdot \mathsf{fma}\left(B, B, t_1\right)\right)}\right)}{B \cdot B + t_1}\\ \mathbf{if}\;B \leq -4.6:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -3.35 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.18 \cdot 10^{-234}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 4
Accuracy	38.7%
Cost	27856

\[\begin{array}{l} t_0 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := \sqrt{2 \cdot \left(C + \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{t_2}{t_0}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-160}:\\ \;\;\;\;-\frac{\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{B \cdot B + t_1}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-241}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{-t_2}{t_0} \cdot \sqrt{F \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 5
Accuracy	39.6%
Cost	27856

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}\\ \mathbf{if}\;B \leq -3.3:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{t_2}{t_1}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot \left(A + \left(C + t_0\right)\right)\right) \cdot \left(F \cdot t_1\right)}}{t_1}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-235}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-31}:\\ \;\;\;\;\frac{-t_2}{t_1} \cdot \sqrt{F \cdot \left(-4 \cdot \left(A \cdot C\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 6
Accuracy	39.6%
Cost	27856

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)\\ t_2 := \mathsf{hypot}\left(B, A - C\right)\\ t_3 := \sqrt{2 \cdot \left(C + \left(A + t_2\right)\right)}\\ t_4 := \mathsf{fma}\left(B, B, t_0\right)\\ \mathbf{if}\;B \leq -2.6:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{t_3}{t_1}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;\sqrt{\left(A + \left(C + t_2\right)\right) \cdot \left(2 \cdot \left(F \cdot t_4\right)\right)} \cdot \frac{1}{-t_4}\\ \mathbf{elif}\;B \leq -2.15 \cdot 10^{-234}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{-t_3}{t_1} \cdot \sqrt{F \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 7
Accuracy	38.3%
Cost	27140

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(\left(A + C\right) + t_0\right)} \cdot \left(B \cdot \sqrt{F}\right)}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-161}:\\ \;\;\;\;-\frac{\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_1}\\ \mathbf{elif}\;B \leq -2.15 \cdot 10^{-234}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-30}:\\ \;\;\;\;-\frac{\sqrt{A + \left(C + t_0\right)} \cdot \sqrt{-2 \cdot \left(4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 8
Accuracy	38.8%
Cost	27140

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-62}:\\ \;\;\;\;\left(B \cdot \sqrt{F}\right) \cdot \frac{\sqrt{2 \cdot \left(C + \left(A + t_0\right)\right)}}{\mathsf{fma}\left(-4, A \cdot C, B \cdot B\right)}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-161}:\\ \;\;\;\;-\frac{\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_1}\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-238}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-32}:\\ \;\;\;\;-\frac{\sqrt{A + \left(C + t_0\right)} \cdot \sqrt{-2 \cdot \left(4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 9
Accuracy	35.9%
Cost	26964

\[\begin{array}{l} t_0 := \sqrt{\frac{-F}{A}}\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := -\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{-2 \cdot \left(4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{if}\;B \leq -2.05 \cdot 10^{-160}:\\ \;\;\;\;-\frac{\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_1}\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-236}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \left(\sqrt{F} \cdot \sqrt{A + \mathsf{hypot}\left(B, A\right)}\right)\\ \end{array} \]

Alternative 10
Accuracy	29.7%
Cost	21716

\[\begin{array}{l} t_0 := \sqrt{\frac{-F}{A}}\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := -\frac{\sqrt{A + \left(C + \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \sqrt{-2 \cdot \left(4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)}}{t_1}\\ \mathbf{if}\;B \leq -4.2 \cdot 10^{-161}:\\ \;\;\;\;-\frac{\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_1}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{B \cdot F}\\ \end{array} \]

Alternative 11
Accuracy	30.0%
Cost	15308

\[\begin{array}{l} t_0 := -\frac{\sqrt{\left(\left(\left(A + C\right) + \mathsf{hypot}\left(A - C, B\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{if}\;B \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-188}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{+104}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{B \cdot F}\\ \end{array} \]

Alternative 12
Accuracy	19.6%
Cost	14620

\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ t_1 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_2 := t_0 \cdot \sqrt{B \cdot F}\\ \mathbf{if}\;C \leq -2 \cdot 10^{+53}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{elif}\;C \leq -1.55 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -1.6 \cdot 10^{-133}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;C \leq -1.12 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -3.7 \cdot 10^{-257}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-A}}\\ \mathbf{elif}\;C \leq 10^{-102}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + A\right)}\right)\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \left(C - A\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \sqrt{F \cdot \left(-0.5 \cdot \frac{B}{\frac{A}{B}}\right)}\\ \end{array} \]

Alternative 13
Accuracy	21.1%
Cost	14604

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{1}{-\mathsf{fma}\left(B, B, t_0\right)} \cdot \sqrt{\left(\left(A \cdot C\right) \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right) \cdot -8}\\ t_2 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;C \leq -5.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.25 \cdot 10^{-99}:\\ \;\;\;\;t_2 \cdot \sqrt{B \cdot F}\\ \mathbf{elif}\;C \leq -2.2 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.02 \cdot 10^{-102}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + A\right)}\right)\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \left(C - A\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{B \cdot B + t_0}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \sqrt{F \cdot \left(-0.5 \cdot \frac{B}{\frac{A}{B}}\right)}\\ \end{array} \]

Alternative 14
Accuracy	20.9%
Cost	14604

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;C \leq -3.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(4 \cdot \left(A \cdot \left(\left(A \cdot C\right) \cdot \left(F \cdot -2\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, C \cdot \left(A \cdot -4\right)\right)}\\ \mathbf{elif}\;C \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;t_1 \cdot \sqrt{B \cdot F}\\ \mathbf{elif}\;C \leq -3.8 \cdot 10^{-133}:\\ \;\;\;\;\frac{1}{-\mathsf{fma}\left(B, B, t_0\right)} \cdot \sqrt{\left(\left(A \cdot C\right) \cdot \left(F \cdot \left(2 \cdot A\right)\right)\right) \cdot -8}\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{-102}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + A\right)}\right)\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \left(C - A\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{B \cdot B + t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(-0.5 \cdot \frac{B}{\frac{A}{B}}\right)}\\ \end{array} \]

Alternative 15
Accuracy	21.1%
Cost	14476

\[\begin{array}{l} t_0 := \frac{\sqrt{2 \cdot \left(\left(A \cdot F\right) \cdot \left(\left(A \cdot C\right) \cdot -8\right)\right)}}{-\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ t_1 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;C \leq -3 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -7.4 \cdot 10^{-98}:\\ \;\;\;\;t_1 \cdot \sqrt{B \cdot F}\\ \mathbf{elif}\;C \leq -2.65 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{-102}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + A\right)}\right)\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \left(C - A\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(-0.5 \cdot \frac{B}{\frac{A}{B}}\right)}\\ \end{array} \]

Alternative 16
Accuracy	22.1%
Cost	13968

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;A \leq -1.25 \cdot 10^{+70}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-A}}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{B \cdot F}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-175}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-119}:\\ \;\;\;\;\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(B + A\right)}\right)\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{+184}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A + C\right) + \left(A - C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 17
Accuracy	22.1%
Cost	13840

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-\sqrt{2}}{B} \cdot \sqrt{B \cdot F}\\ t_2 := F \cdot t_0\\ \mathbf{if}\;A \leq -3.7 \cdot 10^{+70}:\\ \;\;\;\;\frac{\sqrt{F}}{\sqrt{-A}}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -4.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{+181}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(\left(A + C\right) + \left(A - C\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 18
Accuracy	17.5%
Cost	13584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{\sqrt{F}}{\sqrt{-A}}\\ \mathbf{if}\;C \leq -1.66 \cdot 10^{+69}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{elif}\;C \leq -2.1 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -3.6 \cdot 10^{-153}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(A + \left(A + C\right)\right) \cdot \left(4 \cdot \left(F \cdot \left(A \cdot C\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq -1.56 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) - B\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \left(C - A\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_0}\\ \end{array} \]

Alternative 19
Accuracy	16.0%
Cost	8976

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq -3.6 \cdot 10^{-153}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq -2.95 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{-87}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(\left(A + C\right) - B\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 190000:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(\left(A + C\right) + \left(C - A\right)\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right) \cdot -2}}{t_0}\\ \end{array} \]

Alternative 20
Accuracy	15.9%
Cost	8848

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -6.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq -1.26 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(\left(A + C\right) - B\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 410000:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 21
Accuracy	17.0%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ t_1 := \sqrt{\frac{-F}{A}}\\ \mathbf{if}\;A \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-119}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(B + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 22
Accuracy	17.3%
Cost	8584

\[\begin{array}{l} t_0 := B \cdot B + -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;A \leq -2.5 \cdot 10^{-111}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(C + \left(A + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 23
Accuracy	15.0%
Cost	8072

\[\begin{array}{l} \mathbf{if}\;A \leq 3.3 \cdot 10^{-78}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(-8 \cdot \left(A \cdot A\right)\right) \cdot \left(C \cdot F\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \end{array} \]

Alternative 24
Accuracy	14.4%
Cost	7053

\[\begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{+70} \lor \neg \left(C \leq 9.5 \cdot 10^{-102}\right) \land C \leq 115000000000:\\ \;\;\;\;\sqrt{\frac{-F}{C}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{-F}{A}}\\ \end{array} \]

Alternative 25
Accuracy	11.8%
Cost	6656

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

Alternative 26
Accuracy	1.1%
Cost	6592

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

Reproduce

herbie shell --seed 2023131 
(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))))