ABCF->ab-angle b

Average Error: 53.0 → 39.9

Time: 58.0s

Precision: binary64

Cost: 155788

Math

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

↓

\[\begin{array}{l} t_0 := \frac{-\sqrt{\left(\sqrt{{B}^{2} + {\left(A - C\right)}^{2}} - \left(A + C\right)\right) \cdot \left(2 \cdot \left(F \cdot \left(\left(4 \cdot A\right) \cdot C - {B}^{2}\right)\right)\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)}\\ t_1 := F \cdot \left(B \cdot B\right)\\ t_2 := B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\\ t_3 := \mathsf{hypot}\left(B, A - C\right)\\ t_4 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-210}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(A - \left(t_3 - C\right)\right)}\right)}{t_4}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(2, \frac{\mathsf{fma}\left(-0.5, t_1 \cdot t_2, 2 \cdot \left(t_2 \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)\right)}{A}, \mathsf{fma}\left(-8, A \cdot \left(\left(C \cdot F\right) \cdot \left(C + C\right)\right), 2 \cdot \mathsf{fma}\left(2, t_2 \cdot \left(C \cdot F\right), t_1 \cdot \left(C + C\right)\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;t_0 \leq \infty:\\ \;\;\;\;\frac{\sqrt{t_4 \cdot \left(\left(A + C\right) - t_3\right)} \cdot \left(-\sqrt{2 \cdot F}\right)}{t_4}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0
         (/
          (-
           (sqrt
            (*
             (- (sqrt (+ (pow B 2.0) (pow (- A C) 2.0))) (+ A C))
             (* 2.0 (* F (- (* (* 4.0 A) C) (pow B 2.0)))))))
          (+ (pow B 2.0) (* C (* A -4.0)))))
        (t_1 (* F (* B B)))
        (t_2 (+ (* B B) (- (* C C) (pow (- C) 2.0))))
        (t_3 (hypot B (- A C)))
        (t_4 (fma B B (* A (* C -4.0)))))
   (if (<= t_0 -2e-210)
     (/
      (*
       (sqrt (* 2.0 (fma A (* C -4.0) (* B B))))
       (- (sqrt (* F (- A (- t_3 C))))))
      t_4)
     (if (<= t_0 0.0)
       (/
        (-
         (sqrt
          (fma
           2.0
           (/ (fma -0.5 (* t_1 t_2) (* 2.0 (* t_2 (* F (* C C))))) A)
           (fma
            -8.0
            (* A (* (* C F) (+ C C)))
            (* 2.0 (fma 2.0 (* t_2 (* C F)) (* t_1 (+ C C))))))))
        t_4)
       (if (<= t_0 INFINITY)
         (/ (* (sqrt (* t_4 (- (+ A C) t_3))) (- (sqrt (* 2.0 F)))) t_4)
         (* (sqrt (/ F B)) (- (sqrt 2.0))))))))

C

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

↓

double code(double A, double B, double C, double F) {
	double t_0 = -sqrt(((sqrt((pow(B, 2.0) + pow((A - C), 2.0))) - (A + C)) * (2.0 * (F * (((4.0 * A) * C) - pow(B, 2.0)))))) / (pow(B, 2.0) + (C * (A * -4.0)));
	double t_1 = F * (B * B);
	double t_2 = (B * B) + ((C * C) - pow(-C, 2.0));
	double t_3 = hypot(B, (A - C));
	double t_4 = fma(B, B, (A * (C * -4.0)));
	double tmp;
	if (t_0 <= -2e-210) {
		tmp = (sqrt((2.0 * fma(A, (C * -4.0), (B * B)))) * -sqrt((F * (A - (t_3 - C))))) / t_4;
	} else if (t_0 <= 0.0) {
		tmp = -sqrt(fma(2.0, (fma(-0.5, (t_1 * t_2), (2.0 * (t_2 * (F * (C * C))))) / A), fma(-8.0, (A * ((C * F) * (C + C))), (2.0 * fma(2.0, (t_2 * (C * F)), (t_1 * (C + C))))))) / t_4;
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = (sqrt((t_4 * ((A + C) - t_3))) * -sqrt((2.0 * F))) / t_4;
	} else {
		tmp = sqrt((F / B)) * -sqrt(2.0);
	}
	return tmp;
}

Julia

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

↓

function code(A, B, C, F)
	t_0 = Float64(Float64(-sqrt(Float64(Float64(sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0))) - Float64(A + C)) * Float64(2.0 * Float64(F * Float64(Float64(Float64(4.0 * A) * C) - (B ^ 2.0))))))) / Float64((B ^ 2.0) + Float64(C * Float64(A * -4.0))))
	t_1 = Float64(F * Float64(B * B))
	t_2 = Float64(Float64(B * B) + Float64(Float64(C * C) - (Float64(-C) ^ 2.0)))
	t_3 = hypot(B, Float64(A - C))
	t_4 = fma(B, B, Float64(A * Float64(C * -4.0)))
	tmp = 0.0
	if (t_0 <= -2e-210)
		tmp = Float64(Float64(sqrt(Float64(2.0 * fma(A, Float64(C * -4.0), Float64(B * B)))) * Float64(-sqrt(Float64(F * Float64(A - Float64(t_3 - C)))))) / t_4);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(-sqrt(fma(2.0, Float64(fma(-0.5, Float64(t_1 * t_2), Float64(2.0 * Float64(t_2 * Float64(F * Float64(C * C))))) / A), fma(-8.0, Float64(A * Float64(Float64(C * F) * Float64(C + C))), Float64(2.0 * fma(2.0, Float64(t_2 * Float64(C * F)), Float64(t_1 * Float64(C + C)))))))) / t_4);
	elseif (t_0 <= Inf)
		tmp = Float64(Float64(sqrt(Float64(t_4 * Float64(Float64(A + C) - t_3))) * Float64(-sqrt(Float64(2.0 * F)))) / t_4);
	else
		tmp = Float64(sqrt(Float64(F / B)) * Float64(-sqrt(2.0)));
	end
	return tmp
end

Wolfram

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

↓

code[A_, B_, C_, F_] := Block[{t$95$0 = N[((-N[Sqrt[N[(N[(N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(A + C), $MachinePrecision]), $MachinePrecision] * N[(2.0 * N[(F * N[(N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision] - N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / N[(N[Power[B, 2.0], $MachinePrecision] + N[(C * N[(A * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(F * N[(B * B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(B * B), $MachinePrecision] + N[(N[(C * C), $MachinePrecision] - N[Power[(-C), 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$4 = N[(B * B + N[(A * N[(C * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-210], N[(N[(N[Sqrt[N[(2.0 * N[(A * N[(C * -4.0), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(F * N[(A - N[(t$95$3 - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[((-N[Sqrt[N[(2.0 * N[(N[(-0.5 * N[(t$95$1 * t$95$2), $MachinePrecision] + N[(2.0 * N[(t$95$2 * N[(F * N[(C * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision] + N[(-8.0 * N[(A * N[(N[(C * F), $MachinePrecision] * N[(C + C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(2.0 * N[(t$95$2 * N[(C * F), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(C + C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$4), $MachinePrecision], If[LessEqual[t$95$0, Infinity], N[(N[(N[Sqrt[N[(t$95$4 * N[(N[(A + C), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[N[(2.0 * F), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / t$95$4), $MachinePrecision], N[(N[Sqrt[N[(F / B), $MachinePrecision]], $MachinePrecision] * (-N[Sqrt[2.0], $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-210

   1. Initial program 38.8

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

   2. Simplified 33.3

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(C - \left(\mathsf{hypot}\left(B, A - C\right) - A\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 -4 C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 12 points increase in error, 14 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 14 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C)))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C))))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A C)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 19 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= +-commutative_binary64 (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.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))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 (Rewrite=> +-commutative_binary64 (+.f64 C A)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (Rewrite=> associate--l+_binary64 (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 2 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 2 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 26 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C)) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 A C)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C)))))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C)))))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C))))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 22.9

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

   4. Simplified 22.9

      \[\leadsto \frac{-\color{blue}{\sqrt{F \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      Proof
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (fma.f64 A (*.f64 C -4) (*.f64 B B)))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (fma.f64 A (Rewrite<= *-commutative_binary64 (*.f64 -4 C)) (*.f64 B B)))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (fma.f64 A (*.f64 -4 C) (Rewrite<= unpow2_binary64 (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 A (*.f64 -4 C)) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (*.f64 A (*.f64 -4 C)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (+.f64 (Rewrite=> unpow2_binary64 (*.f64 B B)) (*.f64 A (*.f64 -4 C))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (Rewrite=> fma-def_binary64 (fma.f64 B B (*.f64 A (*.f64 -4 C)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 (sqrt.f64 (*.f64 2 (fma.f64 B B (*.f64 A (*.f64 -4 C))))) (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error

   if -2.0000000000000001e-210 < (/.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 61.6

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

   2. Simplified 57.9

      \[\leadsto \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 -4 C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 12 points increase in error, 14 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 14 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C)))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C))))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A C)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 19 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= +-commutative_binary64 (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.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))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 (Rewrite=> +-commutative_binary64 (+.f64 C A)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (Rewrite=> associate--l+_binary64 (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 2 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 2 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 26 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C)) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 A C)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C)))))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C)))))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C))))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in A around inf 46.6

      \[\leadsto \frac{-\sqrt{\color{blue}{2 \cdot \frac{-0.5 \cdot \left(\left(\left({B}^{2} + {C}^{2}\right) - {\left(-1 \cdot C\right)}^{2}\right) \cdot \left(F \cdot {B}^{2}\right)\right) + 2 \cdot \left(\left(\left({B}^{2} + {C}^{2}\right) - {\left(-1 \cdot C\right)}^{2}\right) \cdot \left({C}^{2} \cdot F\right)\right)}{A} + \left(-8 \cdot \left(A \cdot \left(\left(C - -1 \cdot C\right) \cdot \left(C \cdot F\right)\right)\right) + 2 \cdot \left(2 \cdot \left(\left(\left({B}^{2} + {C}^{2}\right) - {\left(-1 \cdot C\right)}^{2}\right) \cdot \left(C \cdot F\right)\right) + \left(C - -1 \cdot C\right) \cdot \left(F \cdot {B}^{2}\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

   4. Simplified 46.7

      \[\leadsto \frac{-\sqrt{\color{blue}{\mathsf{fma}\left(2, \frac{\mathsf{fma}\left(-0.5, \left(F \cdot \left(B \cdot B\right)\right) \cdot \left(B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\right), 2 \cdot \left(\left(F \cdot \left(C \cdot C\right)\right) \cdot \left(B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\right)\right)\right)}{A}, \mathsf{fma}\left(-8, A \cdot \left(\left(F \cdot C\right) \cdot \left(C - \left(-C\right)\right)\right), 2 \cdot \mathsf{fma}\left(2, \left(F \cdot C\right) \cdot \left(B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\right), \left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C - \left(-C\right)\right)\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (*.f64 F (*.f64 B B)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (*.f64 F (Rewrite<= unpow2_binary64 (pow.f64 B 2))) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (*.f64 F (pow.f64 B 2)) (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (*.f64 F (pow.f64 B 2)) (+.f64 (pow.f64 B 2) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 C 2)) (pow.f64 (neg.f64 C) 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (*.f64 F (pow.f64 B 2)) (+.f64 (pow.f64 B 2) (-.f64 (pow.f64 C 2) (pow.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C)) 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (*.f64 F (pow.f64 B 2)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (*.f64 F (*.f64 C C)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (*.f64 (*.f64 F (Rewrite<= unpow2_binary64 (pow.f64 C 2))) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 C 2) F)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (*.f64 (*.f64 (pow.f64 C 2) F) (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (*.f64 (*.f64 (pow.f64 C 2) F) (+.f64 (pow.f64 B 2) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 C 2)) (pow.f64 (neg.f64 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (*.f64 (*.f64 (pow.f64 C 2) F) (+.f64 (pow.f64 B 2) (-.f64 (pow.f64 C 2) (pow.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C)) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (*.f64 (*.f64 (pow.f64 C 2) F) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (fma.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2))) (*.f64 2 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F))))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 F C) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 12 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 C F)) (-.f64 C (neg.f64 C)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 12 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (*.f64 C F) (-.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C))))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F)))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 F C) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 C F)) (+.f64 (*.f64 B B) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 C F) (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (-.f64 (*.f64 C C) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 C F) (+.f64 (pow.f64 B 2) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 C 2)) (pow.f64 (neg.f64 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 C F) (+.f64 (pow.f64 B 2) (-.f64 (pow.f64 C 2) (pow.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C)) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (*.f64 C F) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F))) (*.f64 (*.f64 F (*.f64 B B)) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F)) (*.f64 (*.f64 F (Rewrite<= unpow2_binary64 (pow.f64 B 2))) (-.f64 C (neg.f64 C))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F)) (*.f64 (*.f64 F (pow.f64 B 2)) (-.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C)))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 30 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (fma.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F)) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 F (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 12 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (fma.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F))) (*.f64 2 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F))) (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 F (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 12 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (fma.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F)))) (*.f64 2 (+.f64 (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F))) (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 F (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 F (pow.f64 B 2)))) (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 (pow.f64 C 2) F)))) A)) (+.f64 (*.f64 -8 (*.f64 A (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 C F)))) (*.f64 2 (+.f64 (*.f64 2 (*.f64 (-.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)) (pow.f64 (*.f64 -1 C) 2)) (*.f64 C F))) (*.f64 (-.f64 C (*.f64 -1 C)) (*.f64 F (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 30 points decrease in error

   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 40.0

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

   2. Simplified 28.6

      \[\leadsto \color{blue}{\frac{-\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right) \cdot \left(2 \cdot F\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 -4 C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 12 points increase in error, 14 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 14 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C)))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C))))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A C)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 19 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= +-commutative_binary64 (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.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))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 (Rewrite=> +-commutative_binary64 (+.f64 C A)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (Rewrite=> associate--l+_binary64 (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 2 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 2 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 26 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C)) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 A C)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C)))))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C)))))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C))))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 28.0

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

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

   1. Initial program 64.0

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

   2. Simplified 63.1

      \[\leadsto \color{blue}{\frac{-\sqrt{2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right) \cdot \left(F \cdot \left(C - \left(\mathsf{hypot}\left(B, A - C\right) - A\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 -4 C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 12 points increase in error, 14 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 14 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C))))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C)))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (hypot.f64 B (-.f64 A C)) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C))))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A C)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (-.f64 C (-.f64 (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))) A))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 19 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= +-commutative_binary64 (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (*.f64 F (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.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))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 (Rewrite=> +-commutative_binary64 (+.f64 C A)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (Rewrite=> associate--l+_binary64 (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 2 (*.f64 C (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 2 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) C))) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 26 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C)) (*.f64 2 (*.f64 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) C) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 C (-.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 A C)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) C)))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 C)))))): 0 points increase in error, 34 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 A (*.f64 4 C)))))): 34 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A 4) C))))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (fma.f64 B B (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 A)) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in B around -inf 63.6

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

   4. Simplified 63.6

      \[\leadsto \frac{-\sqrt{2 \cdot \color{blue}{\left(F \cdot \left({B}^{3} + \left(B \cdot B\right) \cdot \left(A + C\right)\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      Proof
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (fma.f64 A (*.f64 C -4) (*.f64 B B)))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (fma.f64 A (Rewrite<= *-commutative_binary64 (*.f64 -4 C)) (*.f64 B B)))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (fma.f64 A (*.f64 -4 C) (Rewrite<= unpow2_binary64 (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 A (*.f64 -4 C)) (pow.f64 B 2))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (*.f64 A (*.f64 -4 C)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (+.f64 (Rewrite=> unpow2_binary64 (*.f64 B B)) (*.f64 A (*.f64 -4 C))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (*.f64 2 (Rewrite=> fma-def_binary64 (fma.f64 B B (*.f64 A (*.f64 -4 C)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 8 points decrease in error
      (/.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 (sqrt.f64 (*.f64 2 (fma.f64 B B (*.f64 A (*.f64 -4 C))))) (sqrt.f64 (*.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 8 points increase in error, 0 points decrease in error

   5. Taylor expanded in C around 0 63.5

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

   6. Simplified 63.5

      \[\leadsto \frac{-\sqrt{2 \cdot \left(F \cdot \color{blue}{\left(\left(B \cdot B\right) \cdot \left(A + B\right)\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(-4 \cdot C\right)\right)} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (*.f64 (*.f64 B B) (+.f64 A B)))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 A (*.f64 B B)) (*.f64 B (*.f64 B B)))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (*.f64 A (Rewrite<= unpow2_binary64 (pow.f64 B 2))) (*.f64 B (*.f64 B B))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 0 points increase in error, 4 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (*.f64 A (pow.f64 B 2)) (Rewrite<= cube-mult_binary64 (pow.f64 B 3))))))) (fma.f64 B B (*.f64 A (*.f64 -4 C)))): 4 points increase in error, 0 points decrease in error

   7. Taylor expanded in A around 0 53.6

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

   8. Simplified 53.6

      \[\leadsto \color{blue}{\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)} \]
      Proof
      (*.f64 (sqrt.f64 (/.f64 F B)) (neg.f64 (sqrt.f64 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (/.f64 F B)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (sqrt.f64 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 -1 (sqrt.f64 2)) (sqrt.f64 (/.f64 F B)))): 0 points increase in error, 4 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 F B))))): 0 points increase in error, 4 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 39.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{-\sqrt{\left(\sqrt{{B}^{2} + {\left(A - C\right)}^{2}} - \left(A + C\right)\right) \cdot \left(2 \cdot \left(F \cdot \left(\left(4 \cdot A\right) \cdot C - {B}^{2}\right)\right)\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq -2 \cdot 10^{-210}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(A - \left(\mathsf{hypot}\left(B, A - C\right) - C\right)\right)}\right)}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;\frac{-\sqrt{\left(\sqrt{{B}^{2} + {\left(A - C\right)}^{2}} - \left(A + C\right)\right) \cdot \left(2 \cdot \left(F \cdot \left(\left(4 \cdot A\right) \cdot C - {B}^{2}\right)\right)\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq 0:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(2, \frac{\mathsf{fma}\left(-0.5, \left(F \cdot \left(B \cdot B\right)\right) \cdot \left(B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\right), 2 \cdot \left(\left(B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\right) \cdot \left(F \cdot \left(C \cdot C\right)\right)\right)\right)}{A}, \mathsf{fma}\left(-8, A \cdot \left(\left(C \cdot F\right) \cdot \left(C + C\right)\right), 2 \cdot \mathsf{fma}\left(2, \left(B \cdot B + \left(C \cdot C - {\left(-C\right)}^{2}\right)\right) \cdot \left(C \cdot F\right), \left(F \cdot \left(B \cdot B\right)\right) \cdot \left(C + C\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;\frac{-\sqrt{\left(\sqrt{{B}^{2} + {\left(A - C\right)}^{2}} - \left(A + C\right)\right) \cdot \left(2 \cdot \left(F \cdot \left(\left(4 \cdot A\right) \cdot C - {B}^{2}\right)\right)\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)} \leq \infty:\\ \;\;\;\;\frac{\sqrt{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(\left(A + C\right) - \mathsf{hypot}\left(B, A - C\right)\right)} \cdot \left(-\sqrt{2 \cdot F}\right)}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	40.4
Cost	155788

\[\begin{array}{l} t_0 := \frac{-\sqrt{\left(\sqrt{{B}^{2} + {\left(A - C\right)}^{2}} - \left(A + C\right)\right) \cdot \left(2 \cdot \left(F \cdot \left(\left(4 \cdot A\right) \cdot C - {B}^{2}\right)\right)\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)}\\ t_1 := \mathsf{hypot}\left(B, A - C\right)\\ t_2 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-210}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(A - \left(t_1 - C\right)\right)}\right)}{t_2}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{-\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(C + C\right)\right)\right)}}{t_2}\\ \mathbf{elif}\;t_0 \leq \infty:\\ \;\;\;\;\frac{\sqrt{t_2 \cdot \left(\left(A + C\right) - t_1\right)} \cdot \left(-\sqrt{2 \cdot F}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 2
Error	40.3
Cost	155788

\[\begin{array}{l} t_0 := B \cdot B + A \cdot A\\ t_1 := {\left(-A\right)}^{2}\\ t_2 := t_0 - t_1\\ t_3 := \frac{-\sqrt{\left(\sqrt{{B}^{2} + {\left(A - C\right)}^{2}} - \left(A + C\right)\right) \cdot \left(2 \cdot \left(F \cdot \left(\left(4 \cdot A\right) \cdot C - {B}^{2}\right)\right)\right)}}{{B}^{2} + C \cdot \left(A \cdot -4\right)}\\ t_4 := \mathsf{hypot}\left(B, A - C\right)\\ t_5 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-210}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(A - \left(t_4 - C\right)\right)}\right)}{t_5}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(-8, A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right), 2 \cdot \left(F \cdot \mathsf{fma}\left(2, A \cdot t_2, \left(B \cdot B\right) \cdot \left(A + A\right)\right) + \frac{F \cdot \mathsf{fma}\left(2, \left(A \cdot A\right) \cdot t_2, \left(\left(B \cdot B\right) \cdot \left(t_1 - t_0\right)\right) \cdot 0.5\right)}{C}\right)\right)}}{t_5}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\frac{\sqrt{t_5 \cdot \left(\left(A + C\right) - t_4\right)} \cdot \left(-\sqrt{2 \cdot F}\right)}{t_5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \end{array} \]

Alternative 3
Error	44.4
Cost	35044

\[\begin{array}{l} t_0 := A \cdot \left(C \cdot -4\right)\\ t_1 := A - \left(\mathsf{hypot}\left(B, A - C\right) - C\right)\\ t_2 := \mathsf{fma}\left(B, B, t_0\right)\\ t_3 := \frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot t_1}\right)}{t_2}\\ t_4 := -4 \cdot \left(A \cdot C\right)\\ t_5 := \frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_4}\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-286}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{\sqrt{t_1 \cdot \left(2 \cdot F\right)} \cdot \left(-\mathsf{hypot}\left(B, \sqrt{t_0}\right)\right)}{t_2}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-267}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-209}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{-1}{A \cdot -4} \cdot \frac{\sqrt{2 \cdot \left(t_1 \cdot \left(F \cdot t_2\right)\right)}}{C}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-158}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_4}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{\left(C \cdot C\right) \cdot \left(A \cdot -8\right)} \cdot \left(-\sqrt{2 \cdot F}\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	43.9
Cost	34648

\[\begin{array}{l} t_0 := A \cdot \left(C \cdot -4\right)\\ t_1 := F \cdot \left(C + C\right)\\ t_2 := \mathsf{hypot}\left(B, A - C\right)\\ t_3 := -4 \cdot \left(A \cdot C\right)\\ t_4 := \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)\\ t_5 := \sqrt{2 \cdot t_4}\\ t_6 := \frac{t_5}{t_4} \cdot \left(-\sqrt{F \cdot \left(\left(A + C\right) - t_2\right)}\right)\\ t_7 := \mathsf{fma}\left(B, B, t_0\right)\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-198}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-298}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot t_1\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-229}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{t_3}\\ \mathbf{elif}\;B \leq 2.75 \cdot 10^{-213}:\\ \;\;\;\;\frac{t_5 \cdot \left(-\sqrt{t_1}\right)}{t_7}\\ \mathbf{elif}\;B \leq 38000000000:\\ \;\;\;\;\frac{-\sqrt{t_7 \cdot \left(\left(A - \left(t_2 - C\right)\right) \cdot \left(2 \cdot F\right)\right)}}{B \cdot B + t_0}\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 5
Error	44.3
Cost	28248

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := A - \left(t_0 - C\right)\\ t_2 := A \cdot \left(C \cdot -4\right)\\ t_3 := \mathsf{fma}\left(B, B, t_2\right)\\ t_4 := \frac{\sqrt{F \cdot t_1} \cdot \left(B \cdot \sqrt{2}\right)}{t_3}\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-135}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(C + C\right)}\right)}{t_3}\\ \mathbf{elif}\;B \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;\frac{-\sqrt{t_3 \cdot \left(t_1 \cdot \left(2 \cdot F\right)\right)}}{B \cdot B + t_2}\\ \mathbf{elif}\;B \leq 10^{-148}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{-4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(t_3 \cdot \left(F \cdot \left(C + \left(A - t_0\right)\right)\right)\right)}}{t_3}\\ \mathbf{else}:\\ \;\;\;\;-t_4\\ \end{array} \]

Alternative 6
Error	44.3
Cost	27864

\[\begin{array}{l} t_0 := A - \left(\mathsf{hypot}\left(B, A - C\right) - C\right)\\ t_1 := A \cdot \left(C \cdot -4\right)\\ t_2 := \mathsf{fma}\left(B, B, t_1\right)\\ t_3 := \frac{-\sqrt{t_2 \cdot \left(t_0 \cdot \left(2 \cdot F\right)\right)}}{B \cdot B + t_1}\\ t_4 := \frac{\sqrt{F \cdot t_0} \cdot \left(B \cdot \sqrt{2}\right)}{t_2}\\ \mathbf{if}\;B \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-77}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{\sqrt{2 \cdot \mathsf{fma}\left(A, C \cdot -4, B \cdot B\right)} \cdot \left(-\sqrt{F \cdot \left(C + C\right)}\right)}{t_2}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-153}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{-4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;-t_4\\ \end{array} \]

Alternative 7
Error	44.1
Cost	27600

\[\begin{array}{l} t_0 := A \cdot \left(C \cdot -4\right)\\ t_1 := \mathsf{fma}\left(B, B, t_0\right)\\ t_2 := A - \left(\mathsf{hypot}\left(B, A - C\right) - C\right)\\ t_3 := \frac{-\sqrt{t_1 \cdot \left(t_2 \cdot \left(2 \cdot F\right)\right)}}{B \cdot B + t_0}\\ \mathbf{if}\;B \leq -5.2 \cdot 10^{+125}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-148}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{-4 \cdot \left(A \cdot C\right)}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{F \cdot t_2} \cdot \left(B \cdot \sqrt{2}\right)}{t_1}\\ \end{array} \]

Alternative 8
Error	45.4
Cost	21581

\[\begin{array}{l} t_0 := A \cdot \left(C \cdot -4\right)\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{+124}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-300} \lor \neg \left(B \leq 1.7 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{-\sqrt{\mathsf{fma}\left(B, B, t_0\right) \cdot \left(\left(A - \left(\mathsf{hypot}\left(B, A - C\right) - C\right)\right) \cdot \left(2 \cdot F\right)\right)}}{B \cdot B + t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{-4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 9
Error	47.7
Cost	21260

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -7 \cdot 10^{-77}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-298}:\\ \;\;\;\;\frac{-\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(C + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-84}:\\ \;\;\;\;-\frac{\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(B \cdot \sqrt{2}\right) \cdot \left(-\sqrt{F \cdot \left(A - \sqrt{B \cdot B + A \cdot A}\right)}\right)}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 10
Error	47.7
Cost	20620

\[\begin{array}{l} t_0 := -\sqrt{2}\\ t_1 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -1.35 \cdot 10^{-78}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot t_0\\ \mathbf{elif}\;B \leq -1.44 \cdot 10^{-300}:\\ \;\;\;\;\frac{-\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(C + C\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-106}:\\ \;\;\;\;-\frac{\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A - \sqrt{B \cdot B + A \cdot A}\right)} \cdot \frac{t_0}{B}\\ \end{array} \]

Alternative 11
Error	49.0
Cost	14476

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -1.85 \cdot 10^{-77}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-77}:\\ \;\;\;\;-\frac{\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(\left(B - C\right) - A\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right)}}{B \cdot B + t_0}\\ \end{array} \]

Alternative 12
Error	49.1
Cost	14476

\[\begin{array}{l} t_0 := \mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)\\ \mathbf{if}\;B \leq -3 \cdot 10^{-78}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-300}:\\ \;\;\;\;\frac{-\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(C + C\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-90}:\\ \;\;\;\;-\frac{\sqrt{-8 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(\left(B - C\right) - A\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right)}}{B \cdot B + -4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 13
Error	49.1
Cost	13316

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-77}:\\ \;\;\;\;\sqrt{\frac{F}{B}} \cdot \left(-\sqrt{2}\right)\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-89}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(\left(B - C\right) - A\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right)}}{B \cdot B + t_0}\\ \end{array} \]

Alternative 14
Error	54.9
Cost	8716

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;B \leq -115:\\ \;\;\;\;-2 \cdot \sqrt{\frac{F}{B} \cdot \frac{A}{B}}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-298}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_0}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-94}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(\left(B - C\right) - A\right) \cdot \left(F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\right)\right)}}{B \cdot B + t_0}\\ \end{array} \]

Alternative 15
Error	54.3
Cost	8716

\[\begin{array}{l} t_0 := F \cdot \left(4 \cdot \left(A \cdot C\right) - B \cdot B\right)\\ t_1 := -4 \cdot \left(A \cdot C\right)\\ t_2 := B \cdot B + t_1\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(\left(A + \left(B + C\right)\right) \cdot t_0\right)}}{t_2}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-299}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_1}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(\left(B - C\right) - A\right) \cdot t_0\right)}}{t_2}\\ \end{array} \]

Alternative 16
Error	54.4
Cost	8209

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;A \leq -6.8 \cdot 10^{+110}:\\ \;\;\;\;-2 \cdot \sqrt{\frac{F}{B} \cdot \frac{A}{B}}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-5} \lor \neg \left(A \leq 3.15 \cdot 10^{-138}\right) \land A \leq 64000:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 17
Error	54.5
Cost	8080

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ t_1 := \frac{-\sqrt{2 \cdot \left(-8 \cdot \left(\left(C \cdot F\right) \cdot \left(A \cdot A\right)\right)\right)}}{t_0}\\ \mathbf{if}\;A \leq -3.8 \cdot 10^{+111}:\\ \;\;\;\;-2 \cdot \sqrt{\frac{F}{B} \cdot \frac{A}{B}}\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(F \cdot \left(B \cdot \left(B \cdot \left(B + C\right)\right)\right)\right)}}{B \cdot B}\\ \mathbf{elif}\;A \leq 300:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{-2 \cdot \left(\left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right) \cdot 8\right)}}{t_0}\\ \end{array} \]

Alternative 18
Error	53.7
Cost	7812

\[\begin{array}{l} t_0 := -4 \cdot \left(A \cdot C\right)\\ \mathbf{if}\;C \leq 2.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{-\sqrt{-2 \cdot \left(4 \cdot \left(A \cdot \left(C \cdot \left(F \cdot \left(C + C\right)\right)\right)\right)\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{2 \cdot \left(-4 \cdot \left(A \cdot \left(\left(C \cdot F\right) \cdot \left(A + A\right)\right)\right)\right)}}{t_0}\\ \end{array} \]

Alternative 19
Error	59.2
Cost	7688

\[\begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;-2 \cdot \sqrt{\frac{F}{B} \cdot \frac{A}{B}}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(F \cdot \left(B \cdot \left(B \cdot \left(B + C\right)\right)\right)\right)}}{B \cdot B}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\sqrt{A \cdot F}}{B}\\ \end{array} \]

Alternative 20
Error	56.6
Cost	7684

\[\begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{-126}:\\ \;\;\;\;-2 \cdot \sqrt{\frac{F}{B} \cdot \frac{A}{B}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\sqrt{-2 \cdot \left(\left(A \cdot \left(F \cdot \left(C \cdot C\right)\right)\right) \cdot 8\right)}}{-4 \cdot \left(A \cdot C\right)}\\ \end{array} \]

Alternative 21
Error	60.6
Cost	6976

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

Alternative 22
Error	62.1
Cost	6848

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

Reproduce

herbie shell --seed 2022343 
(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))))