ABCF->ab-angle b

Average Error: 81.32% → 66.86%

Time: 1.2min

Precision: binary64

Cost: 67032

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := F \cdot \left(C + \left(A - t_0\right)\right)\\ t_2 := C - t_0\\ t_3 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_4 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ t_5 := -\sqrt{2}\\ t_6 := \sqrt[3]{t_2}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_4}\\ \mathbf{elif}\;B \leq -1.68 \cdot 10^{-90}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-241}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)} \cdot t_5}{t_4}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{t_3 \cdot \left(\left(2 \cdot F\right) \cdot \left(A + t_2\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-154}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot t_1}}{\mathsf{hypot}\left(B, \sqrt{C \cdot \left(A \cdot -4\right)}\right)}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{\sqrt{F \cdot \mathsf{fma}\left({t_6}^{2}, t_6, A\right)} \cdot \left(-\sqrt{2 \cdot t_3}\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_5}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

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 (hypot B (- A C)))
        (t_1 (* F (+ C (- A t_0))))
        (t_2 (- C t_0))
        (t_3 (fma B B (* A (* C -4.0))))
        (t_4 (hypot B (sqrt (* -4.0 (* C A)))))
        (t_5 (- (sqrt 2.0)))
        (t_6 (cbrt t_2)))
   (if (<= B -6.8e+101)
     (/ (- (sqrt (* B (* 2.0 F)))) t_4)
     (if (<= B -1.68e-90)
       (/ (- (sqrt (* 2.0 (* t_3 t_1)))) t_3)
       (if (<= B -4.2e-241)
         (/ (* (sqrt (* F (- C (hypot C B)))) t_5) t_4)
         (if (<= B 1.2e-267)
           (/ (- (sqrt (* t_3 (* (* 2.0 F) (+ A t_2))))) t_3)
           (if (<= B 1.4e-154)
             (/ (- (sqrt (* 2.0 t_1))) (hypot B (sqrt (* C (* A -4.0)))))
             (if (<= B 2.5e+136)
               (/
                (*
                 (sqrt (* F (fma (pow t_6 2.0) t_6 A)))
                 (- (sqrt (* 2.0 t_3))))
                t_3)
               (* (/ t_5 B) (sqrt (* F (- C 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 = hypot(B, (A - C));
	double t_1 = F * (C + (A - t_0));
	double t_2 = C - t_0;
	double t_3 = fma(B, B, (A * (C * -4.0)));
	double t_4 = hypot(B, sqrt((-4.0 * (C * A))));
	double t_5 = -sqrt(2.0);
	double t_6 = cbrt(t_2);
	double tmp;
	if (B <= -6.8e+101) {
		tmp = -sqrt((B * (2.0 * F))) / t_4;
	} else if (B <= -1.68e-90) {
		tmp = -sqrt((2.0 * (t_3 * t_1))) / t_3;
	} else if (B <= -4.2e-241) {
		tmp = (sqrt((F * (C - hypot(C, B)))) * t_5) / t_4;
	} else if (B <= 1.2e-267) {
		tmp = -sqrt((t_3 * ((2.0 * F) * (A + t_2)))) / t_3;
	} else if (B <= 1.4e-154) {
		tmp = -sqrt((2.0 * t_1)) / hypot(B, sqrt((C * (A * -4.0))));
	} else if (B <= 2.5e+136) {
		tmp = (sqrt((F * fma(pow(t_6, 2.0), t_6, A))) * -sqrt((2.0 * t_3))) / t_3;
	} else {
		tmp = (t_5 / B) * sqrt((F * (C - 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 = hypot(B, Float64(A - C))
	t_1 = Float64(F * Float64(C + Float64(A - t_0)))
	t_2 = Float64(C - t_0)
	t_3 = fma(B, B, Float64(A * Float64(C * -4.0)))
	t_4 = hypot(B, sqrt(Float64(-4.0 * Float64(C * A))))
	t_5 = Float64(-sqrt(2.0))
	t_6 = cbrt(t_2)
	tmp = 0.0
	if (B <= -6.8e+101)
		tmp = Float64(Float64(-sqrt(Float64(B * Float64(2.0 * F)))) / t_4);
	elseif (B <= -1.68e-90)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * Float64(t_3 * t_1)))) / t_3);
	elseif (B <= -4.2e-241)
		tmp = Float64(Float64(sqrt(Float64(F * Float64(C - hypot(C, B)))) * t_5) / t_4);
	elseif (B <= 1.2e-267)
		tmp = Float64(Float64(-sqrt(Float64(t_3 * Float64(Float64(2.0 * F) * Float64(A + t_2))))) / t_3);
	elseif (B <= 1.4e-154)
		tmp = Float64(Float64(-sqrt(Float64(2.0 * t_1))) / hypot(B, sqrt(Float64(C * Float64(A * -4.0)))));
	elseif (B <= 2.5e+136)
		tmp = Float64(Float64(sqrt(Float64(F * fma((t_6 ^ 2.0), t_6, A))) * Float64(-sqrt(Float64(2.0 * t_3)))) / t_3);
	else
		tmp = Float64(Float64(t_5 / B) * sqrt(Float64(F * Float64(C - 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[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$1 = N[(F * N[(C + N[(A - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(C - t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(B * B + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[B ^ 2 + N[Sqrt[N[(-4.0 * N[(C * A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$5 = (-N[Sqrt[2.0], $MachinePrecision])}, Block[{t$95$6 = N[Power[t$95$2, 1/3], $MachinePrecision]}, If[LessEqual[B, -6.8e+101], N[((-N[Sqrt[N[(B * N[(2.0 * F), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$4), $MachinePrecision], If[LessEqual[B, -1.68e-90], N[((-N[Sqrt[N[(2.0 * N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision], If[LessEqual[B, -4.2e-241], N[(N[(N[Sqrt[N[(F * N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$5), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[B, 1.2e-267], N[((-N[Sqrt[N[(t$95$3 * N[(N[(2.0 * F), $MachinePrecision] * N[(A + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$3), $MachinePrecision], If[LessEqual[B, 1.4e-154], N[((-N[Sqrt[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]) / N[Sqrt[B ^ 2 + N[Sqrt[N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e+136], N[(N[(N[Sqrt[N[(F * N[(N[Power[t$95$6, 2.0], $MachinePrecision] * t$95$6 + A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(2.0 * t$95$3), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$3), $MachinePrecision], N[(N[(t$95$5 / B), $MachinePrecision] * N[Sqrt[N[(F * N[(C - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -6.80000000000000034e101

   1. Initial program 94.73

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

   2. Simplified 93.92

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

      [Start] 94.73	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 91.25

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

   4. Simplified 91.25

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

      [Start] 91.25	\[ \frac{-\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right) \cdot \sqrt{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 91.25	\[ \frac{-\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(A \cdot C\right) \cdot -4}}\right) \cdot \sqrt{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   5. Applied egg-rr 69.93

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

   6. Simplified 69.65

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

      [Start] 69.93	\[ \frac{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \]
      *-inverses [=>] 69.65	\[ \color{blue}{1} \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \]
      associate-*r* [=>] 69.65	\[ 1 \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(A \cdot C\right) \cdot -4}}\right)} \]
      *-commutative [=>] 69.65	\[ 1 \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(C \cdot A\right)} \cdot -4}\right)} \]

   7. Taylor expanded in B around -inf 73.57

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

   if -6.80000000000000034e101 < B < -1.6799999999999999e-90

   1. Initial program 65.51

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

   2. Simplified 57.44

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

      [Start] 65.51	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   if -1.6799999999999999e-90 < B < -4.1999999999999999e-241

   1. Initial program 80.04

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

   2. Simplified 70.18

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

      [Start] 80.04	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 79.27

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

   4. Simplified 79.28

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

      [Start] 79.27	\[ \frac{-\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right) \cdot \sqrt{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 79.28	\[ \frac{-\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(A \cdot C\right) \cdot -4}}\right) \cdot \sqrt{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   5. Applied egg-rr 76.42

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

   6. Simplified 76.22

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

      [Start] 76.42	\[ \frac{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \]
      *-inverses [=>] 76.22	\[ \color{blue}{1} \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \]
      associate-*r* [=>] 76.22	\[ 1 \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(A \cdot C\right) \cdot -4}}\right)} \]
      *-commutative [=>] 76.22	\[ 1 \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(C \cdot A\right)} \cdot -4}\right)} \]

   7. Taylor expanded in A around 0 86.57

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

   8. Simplified 82.21

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

      [Start] 86.57	\[ 1 \cdot \frac{-\sqrt{\left(C - \sqrt{{B}^{2} + {C}^{2}}\right) \cdot F} \cdot \sqrt{2}}{\mathsf{hypot}\left(B, \sqrt{\left(C \cdot A\right) \cdot -4}\right)} \]
      +-commutative [=>] 86.57	\[ 1 \cdot \frac{-\sqrt{\left(C - \sqrt{\color{blue}{{C}^{2} + {B}^{2}}}\right) \cdot F} \cdot \sqrt{2}}{\mathsf{hypot}\left(B, \sqrt{\left(C \cdot A\right) \cdot -4}\right)} \]
      unpow2 [=>] 86.57	\[ 1 \cdot \frac{-\sqrt{\left(C - \sqrt{\color{blue}{C \cdot C} + {B}^{2}}\right) \cdot F} \cdot \sqrt{2}}{\mathsf{hypot}\left(B, \sqrt{\left(C \cdot A\right) \cdot -4}\right)} \]
      unpow2 [=>] 86.57	\[ 1 \cdot \frac{-\sqrt{\left(C - \sqrt{C \cdot C + \color{blue}{B \cdot B}}\right) \cdot F} \cdot \sqrt{2}}{\mathsf{hypot}\left(B, \sqrt{\left(C \cdot A\right) \cdot -4}\right)} \]
      hypot-def [=>] 82.21	\[ 1 \cdot \frac{-\sqrt{\left(C - \color{blue}{\mathsf{hypot}\left(C, B\right)}\right) \cdot F} \cdot \sqrt{2}}{\mathsf{hypot}\left(B, \sqrt{\left(C \cdot A\right) \cdot -4}\right)} \]

   if -4.1999999999999999e-241 < B < 1.1999999999999999e-267

   1. Initial program 82.6

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

   2. Simplified 72.22

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

      [Start] 82.6	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   if 1.1999999999999999e-267 < B < 1.40000000000000006e-154

   1. Initial program 85.05

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

   2. Simplified 76.76

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

      [Start] 85.05	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 84.99

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

   4. Simplified 84.99

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

      [Start] 84.99	\[ \frac{-\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right) \cdot \sqrt{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      associate-*r* [=>] 84.99	\[ \frac{-\mathsf{hypot}\left(B, \sqrt{\color{blue}{\left(A \cdot C\right) \cdot -4}}\right) \cdot \sqrt{\left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   5. Applied egg-rr 80.84

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

   6. Simplified 80.43

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

      [Start] 80.84	\[ \frac{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \cdot \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \]
      *-commutative [=>] 80.84	\[ \color{blue}{\frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \cdot \frac{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}} \]
      *-inverses [=>] 80.65	\[ \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)} \cdot \color{blue}{1} \]
      associate-/r/ [<=] 80.65	\[ \color{blue}{\frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\frac{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}{1}}} \]
      /-rgt-identity [=>] 80.65	\[ \frac{-\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\color{blue}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}} \]
      distribute-frac-neg [=>] 80.65	\[ \color{blue}{-\frac{\sqrt{\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{A \cdot \left(C \cdot -4\right)}\right)}} \]

   if 1.40000000000000006e-154 < B < 2.5000000000000001e136

   1. Initial program 71.22

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

   2. Simplified 64.15

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

      [Start] 71.22	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Applied egg-rr 59.17

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

   4. Simplified 59.17

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

      [Start] 59.17	\[ \frac{-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \cdot \sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 59.17	\[ \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      *-commutative [=>] 59.17	\[ \frac{-\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \color{blue}{\left(C \cdot -4\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   5. Applied egg-rr 59.56

      \[\leadsto \frac{-\sqrt{F \cdot \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{C - \mathsf{hypot}\left(B, A - C\right)}\right)}^{2}, \sqrt[3]{C - \mathsf{hypot}\left(B, A - C\right)}, A\right)}} \cdot \sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]

   if 2.5000000000000001e136 < B

   1. Initial program 98.41

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

   2. Simplified 98.41

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

      [Start] 98.41	\[ \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]

   3. Taylor expanded in C around 0 98.38

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

   4. Simplified 98.38

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

      [Start] 98.38	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(A + \left(C - \sqrt{{B}^{2} + {A}^{2}}\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 98.38	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(A + \left(C - \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]
      unpow2 [=>] 98.38	\[ \frac{-\sqrt{2 \cdot \left(\left(\left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right) \cdot F\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)\right)\right)}}{B \cdot B - 4 \cdot \left(A \cdot C\right)} \]

   5. Taylor expanded in A around 0 56.67

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

   6. Simplified 56.67

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

      [Start] 56.67	\[ -1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{\left(C - B\right) \cdot F}\right) \]
      associate-*r* [=>] 56.67	\[ \color{blue}{\left(-1 \cdot \frac{\sqrt{2}}{B}\right) \cdot \sqrt{\left(C - B\right) \cdot F}} \]
      associate-*r/ [=>] 56.67	\[ \color{blue}{\frac{-1 \cdot \sqrt{2}}{B}} \cdot \sqrt{\left(C - B\right) \cdot F} \]
      mul-1-neg [=>] 56.67	\[ \frac{\color{blue}{-\sqrt{2}}}{B} \cdot \sqrt{\left(C - B\right) \cdot F} \]
      *-commutative [<=] 56.67	\[ \frac{-\sqrt{2}}{B} \cdot \sqrt{\color{blue}{F \cdot \left(C - B\right)}} \]

3. Recombined 7 regimes into one program.

4. Final simplification 66.86

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)}\\ \mathbf{elif}\;B \leq -1.68 \cdot 10^{-90}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(F \cdot \left(C + \left(A - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-241}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)} \cdot \left(-\sqrt{2}\right)}{\mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-154}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(F \cdot \left(C + \left(A - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{hypot}\left(B, \sqrt{C \cdot \left(A \cdot -4\right)}\right)}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{\sqrt{F \cdot \mathsf{fma}\left({\left(\sqrt[3]{C - \mathsf{hypot}\left(B, A - C\right)}\right)}^{2}, \sqrt[3]{C - \mathsf{hypot}\left(B, A - C\right)}, A\right)} \cdot \left(-\sqrt{2 \cdot \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\right)}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	67.07%
Cost	34648

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := F \cdot \left(C + \left(A - t_0\right)\right)\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_3 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ t_4 := -\sqrt{2}\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_3}\\ \mathbf{elif}\;B \leq -1.85 \cdot 10^{-90}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot t_1\right)}}{t_2}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-241}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)} \cdot t_4}{t_3}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{t_2 \cdot \left(\left(2 \cdot F\right) \cdot \left(A + \left(C - t_0\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot t_1}}{\mathsf{hypot}\left(B, \sqrt{C \cdot \left(A \cdot -4\right)}\right)}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{+123}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(C + A\right) - t_0\right)} \cdot \frac{-\sqrt{2 \cdot t_2}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_4}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 2
Error	66.78%
Cost	34648

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := F \cdot \left(C + \left(A - t_0\right)\right)\\ t_2 := A + \left(C - t_0\right)\\ t_3 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_4 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ t_5 := -\sqrt{2}\\ \mathbf{if}\;B \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_4}\\ \mathbf{elif}\;B \leq -1.68 \cdot 10^{-90}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq -4.1 \cdot 10^{-241}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)} \cdot t_5}{t_4}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{t_3 \cdot \left(\left(2 \cdot F\right) \cdot t_2\right)}}{t_3}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-161}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot t_1}}{\mathsf{hypot}\left(B, \sqrt{C \cdot \left(A \cdot -4\right)}\right)}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{\sqrt{2 \cdot t_3} \cdot \left(-\sqrt{F \cdot t_2}\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_5}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 3
Error	67.64%
Cost	33420

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := F \cdot \left(C + \left(A - t_0\right)\right)\\ t_2 := A + \left(C - t_0\right)\\ t_3 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_4 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ t_5 := -\sqrt{2}\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_4}\\ \mathbf{elif}\;B \leq -1.76 \cdot 10^{-90}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-241}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)} \cdot t_5}{t_4}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{t_3 \cdot \left(\left(2 \cdot F\right) \cdot t_2\right)}}{t_3}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-18}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot t_1}}{\mathsf{hypot}\left(B, \sqrt{C \cdot \left(A \cdot -4\right)}\right)}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_2} \cdot \left(B \cdot t_5\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_5}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 4
Error	67.15%
Cost	27984

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := -\sqrt{2}\\ t_2 := A + \left(C - t_0\right)\\ t_3 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_4 := \frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(C + \left(A - t_0\right)\right)\right)\right)}}{t_3}\\ t_5 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ \mathbf{if}\;B \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_5}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-149}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-241}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot F\right) \cdot \mathsf{fma}\left(-0.5, B \cdot \frac{B}{A - C}, 2 \cdot C\right)}}{t_5}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-288}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot F\right) \cdot t_2}}{t_5}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_2} \cdot \left(B \cdot t_1\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 5
Error	66.9%
Cost	27984

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := F \cdot \left(C + \left(A - t_0\right)\right)\\ t_2 := A + \left(C - t_0\right)\\ t_3 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_4 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ t_5 := -\sqrt{2}\\ \mathbf{if}\;B \leq -3.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_4}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-147}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot t_1\right)}}{t_3}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot F\right) \cdot \mathsf{fma}\left(-0.5, B \cdot \frac{B}{A - C}, 2 \cdot C\right)}}{t_4}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-267}:\\ \;\;\;\;\frac{-\sqrt{t_3 \cdot \left(\left(2 \cdot F\right) \cdot t_2\right)}}{t_3}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot t_1}}{\mathsf{hypot}\left(B, \sqrt{C \cdot \left(A \cdot -4\right)}\right)}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_2} \cdot \left(B \cdot t_5\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_5}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 6
Error	67.29%
Cost	27864

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := -\sqrt{2}\\ t_3 := A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\\ t_4 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ t_5 := \frac{-\sqrt{\left(2 \cdot F\right) \cdot t_3}}{t_4}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_4}\\ \mathbf{elif}\;B \leq -64000000000000:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(B, B, t_0\right)} \cdot \left(\sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)} \cdot \left(B \cdot \sqrt{2}\right)\right)\\ \mathbf{elif}\;B \leq -1.38 \cdot 10^{-201}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-288}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 1.46 \cdot 10^{-18}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sqrt{F \cdot t_3} \cdot \left(B \cdot t_2\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 7
Error	68.6%
Cost	27540

\[\begin{array}{l} t_0 := C \cdot \left(A \cdot -4\right)\\ t_1 := -4 \cdot \left(C \cdot A\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(F \cdot \left(C + \left(A - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{hypot}\left(B, \sqrt{t_0}\right)}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{t_1}\right)}\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;\sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)} \cdot \frac{B}{\frac{\mathsf{fma}\left(B, B, t_1\right)}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -5.8 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-286}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6.1 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 8
Error	68.6%
Cost	27540

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := C \cdot \left(A \cdot -4\right)\\ t_2 := \frac{-\sqrt{2 \cdot \left(F \cdot \left(C + \left(A - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)}}{\mathsf{hypot}\left(B, \sqrt{t_1}\right)}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{t_0}\right)}\\ \mathbf{elif}\;B \leq -3300000000000:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(B, B, t_0\right)} \cdot \left(\sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)} \cdot \left(B \cdot \sqrt{2}\right)\right)\\ \mathbf{elif}\;B \leq -4.05 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-288}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 9
Error	68.64%
Cost	27540

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ t_2 := \frac{-\sqrt{\left(2 \cdot F\right) \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)}}{t_1}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_1}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(B, B, t_0\right)} \cdot \left(\sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)} \cdot \left(B \cdot \sqrt{2}\right)\right)\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-286}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 10
Error	71.02%
Cost	27020

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_1}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-25}:\\ \;\;\;\;\sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)} \cdot \frac{B}{\frac{\mathsf{fma}\left(B, B, t_0\right)}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq -8.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{-\sqrt{\left(2 \cdot F\right) \cdot \left(A - \mathsf{hypot}\left(B, A\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 11
Error	70.79%
Cost	27016

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{t_0}\right)}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-46}:\\ \;\;\;\;\sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)} \cdot \frac{B}{\frac{\mathsf{fma}\left(B, B, t_0\right)}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 12
Error	71.39%
Cost	22096

\[\begin{array}{l} t_0 := -\sqrt{2}\\ t_1 := -4 \cdot \left(C \cdot A\right)\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_3 := \mathsf{hypot}\left(B, \sqrt{t_1}\right)\\ t_4 := t_1 + B \cdot B\\ t_5 := \frac{-\sqrt{2 \cdot \left(\left(F \cdot t_4\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)}}{t_4}\\ \mathbf{if}\;B \leq -1.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_3}\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-243}:\\ \;\;\;\;\frac{-\sqrt{C \cdot \left(F \cdot 4\right) - \frac{F}{\frac{\frac{A}{B}}{B}}}}{t_3}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-90}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(F \cdot \left(C \cdot 4\right)\right)} \cdot \frac{-1}{t_2}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{+135}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \sqrt{B \cdot B + C \cdot C}\right)} \cdot \left(B \cdot t_0\right)}{t_4}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 13
Error	72.2%
Cost	21524

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := -\sqrt{2}\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_3 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ \mathbf{if}\;B \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_3}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{-\sqrt{t_2 \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot A\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -8.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{-\sqrt{C \cdot \left(F \cdot 4\right) - \frac{F}{\frac{\frac{A}{B}}{B}}}}{t_3}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-67}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(F \cdot \left(C \cdot 4\right)\right)} \cdot \frac{-1}{t_2}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{+113}:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \sqrt{B \cdot B + C \cdot C}\right)} \cdot \left(B \cdot t_1\right)}{t_0 + B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 14
Error	71.16%
Cost	21200

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \frac{-\sqrt{2}}{B}\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_3 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ t_4 := t_0 + B \cdot B\\ \mathbf{if}\;B \leq -7 \cdot 10^{+59}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_3}\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-118}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_4\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + A \cdot A}\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-215}:\\ \;\;\;\;\frac{-\sqrt{C \cdot \left(F \cdot 4\right) - \frac{F}{\frac{\frac{A}{B}}{B}}}}{t_3}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(F \cdot \left(C \cdot 4\right)\right)} \cdot \frac{-1}{t_2}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{+118}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(C - \sqrt{B \cdot B + C \cdot C}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 15
Error	72.13%
Cost	21200

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, \sqrt{-4 \cdot \left(C \cdot A\right)}\right)\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ t_2 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_0}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-135}:\\ \;\;\;\;\frac{-\sqrt{t_1 \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot A\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-205}:\\ \;\;\;\;\frac{-\sqrt{C \cdot \left(F \cdot 4\right) - \frac{F}{\frac{\frac{A}{B}}{B}}}}{t_0}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-68}:\\ \;\;\;\;\sqrt{t_1 \cdot \left(F \cdot \left(C \cdot 4\right)\right)} \cdot \frac{-1}{t_1}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{+112}:\\ \;\;\;\;t_2 \cdot \sqrt{F \cdot \left(C - \sqrt{B \cdot B + C \cdot C}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 16
Error	71.27%
Cost	20940

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \frac{-\sqrt{2}}{B}\\ t_2 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ t_3 := t_0 + B \cdot B\\ \mathbf{if}\;B \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_2}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-119}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_3\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + A \cdot A}\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-212}:\\ \;\;\;\;\frac{-\sqrt{C \cdot \left(F \cdot 4\right) - \frac{F}{\frac{\frac{A}{B}}{B}}}}{t_2}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-63}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+117}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(C - \sqrt{B \cdot B + C \cdot C}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 17
Error	73.69%
Cost	20428

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{\mathsf{hypot}\left(B, \sqrt{t_0}\right)}\\ t_2 := t_0 + B \cdot B\\ \mathbf{if}\;B \leq -1.65 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-134}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_2\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + A \cdot A}\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 18
Error	73.47%
Cost	20364

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right)\\ t_1 := \mathsf{hypot}\left(B, \sqrt{t_0}\right)\\ t_2 := t_0 + B \cdot B\\ \mathbf{if}\;B \leq -6 \cdot 10^{+58}:\\ \;\;\;\;\frac{-\sqrt{B \cdot \left(2 \cdot F\right)}}{t_1}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_2\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + A \cdot A}\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{\sqrt{F \cdot C} \cdot -2}{t_1}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 19
Error	76.32%
Cost	15236

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;B \leq -7.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - \sqrt{B \cdot B + A \cdot A}\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 20
Error	76.54%
Cost	14852

\[\begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(A + \left(C - \sqrt{B \cdot B + A \cdot A}\right)\right) \cdot \left(B \cdot \left(B \cdot F\right)\right)\right)}}{-4 \cdot \left(C \cdot A\right) + B \cdot B}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 21
Error	76.92%
Cost	14472

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;B \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(2 \cdot F\right) \cdot \left(2 \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 22
Error	76.86%
Cost	14472

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-4 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 23
Error	78.12%
Cost	14344

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;B \leq -7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{-\sqrt{\left(A \cdot -8\right) \cdot \left(\left(F \cdot C\right) \cdot \left(C + C\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 24
Error	77.96%
Cost	14216

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;B \leq -5.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-217}:\\ \;\;\;\;\frac{-\sqrt{A \cdot \left(\left(F \cdot C\right) \cdot \left(A \cdot -16\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 25
Error	79.21%
Cost	14216

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;B \leq -2.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 4.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{-\sqrt{\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(A \cdot -16\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 26
Error	79.1%
Cost	13704

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -1.65 \cdot 10^{-133}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-73}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(\left(C - A\right) + \frac{B \cdot B}{C} \cdot 0.5\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C - B\right)}\\ \end{array} \]

Alternative 27
Error	88.37%
Cost	8716

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ t_1 := F \cdot t_0\\ t_2 := \frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;B \leq -7.5 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-272}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C - B\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 28
Error	85.79%
Cost	8716

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ t_1 := \frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ t_2 := F \cdot t_0\\ \mathbf{if}\;A \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7.6 \cdot 10^{-115}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_2 \cdot \left(A + \left(B + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(A \cdot \left(-4 \cdot \left(C \cdot \left(F \cdot C\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 29
Error	82.53%
Cost	8584

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{-161}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \end{array} \]

Alternative 30
Error	82.51%
Cost	8584

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ t_1 := F \cdot t_0\\ \mathbf{if}\;C \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + \left(C - A\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_1 \cdot \left(A + \left(C + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \end{array} \]

Alternative 31
Error	88.36%
Cost	8452

\[\begin{array}{l} t_0 := -4 \cdot \left(C \cdot A\right) + B \cdot B\\ \mathbf{if}\;C \leq 3.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot t_0\right) \cdot \left(A + \left(C - B\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \end{array} \]

Alternative 32
Error	90.8%
Cost	7556

\[\begin{array}{l} \mathbf{if}\;C \leq 7.5 \cdot 10^{-168}:\\ \;\;\;\;\frac{\sqrt{F \cdot C} \cdot -2}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{C \cdot \left(A \cdot -4\right)}\\ \end{array} \]

Alternative 33
Error	96.87%
Cost	6848

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

Alternative 34
Error	96.91%
Cost	6848

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

Reproduce

herbie shell --seed 2023102 
(FPCore (A B C F)
  :name "ABCF->ab-angle b"
  :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))))