Average Error: 52.2 → 38.2
Time: 45.5s
Precision: binary64
Cost: 68172
\[ \begin{array}{c}[A, C] = \mathsf{sort}([A, C])\\ \end{array} \]
\[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
↓
\[\begin{array}{l} t_0 := A - \mathsf{hypot}\left(A, B\right)\\ t_1 := F \cdot t_0\\ \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot \frac{-\sqrt{2}}{B}\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot \sqrt{\frac{\frac{1}{F}}{t_0}}\right) \cdot \left(\left(C \cdot \sqrt{2}\right) \cdot \left(B \cdot \left(\frac{F}{B \cdot B} \cdot \left(1 + A \cdot \sqrt{\frac{1}{\mathsf{fma}\left(A, A, B \cdot B\right)}}\right) + 4 \cdot \left(\frac{A}{{B}^{4}} \cdot t_1\right)\right)\right)\right) - \frac{\sqrt{2}}{B} \cdot \sqrt{t_1}\\ \end{array} \]
(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 (- A (hypot A B))) (t_1 (* F t_0)))
   (if (<= B -28032165908107884.0)
     (/ (sqrt (* F (- C (hypot C B)))) (/ B (sqrt 2.0)))
     (if (<= B 2.15e-135)
       (-
        (/ (sqrt (* -16.0 (* (* C A) (* F A)))) (+ (* B B) (* (* C A) -4.0))))
       (if (<= B 1.55e+100)
         (* (sqrt (* F (* (* B B) (/ -0.5 C)))) (/ (- (sqrt 2.0)) B))
         (-
          (*
           (* -0.5 (sqrt (/ (/ 1.0 F) t_0)))
           (*
            (* C (sqrt 2.0))
            (*
             B
             (+
              (* (/ F (* B B)) (+ 1.0 (* A (sqrt (/ 1.0 (fma A A (* B B)))))))
              (* 4.0 (* (/ A (pow B 4.0)) t_1))))))
          (* (/ (sqrt 2.0) B) (sqrt t_1))))))))
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 = A - hypot(A, B);
	double t_1 = F * t_0;
	double tmp;
	if (B <= -28032165908107884.0) {
		tmp = sqrt((F * (C - hypot(C, B)))) / (B / sqrt(2.0));
	} else if (B <= 2.15e-135) {
		tmp = -(sqrt((-16.0 * ((C * A) * (F * A)))) / ((B * B) + ((C * A) * -4.0)));
	} else if (B <= 1.55e+100) {
		tmp = sqrt((F * ((B * B) * (-0.5 / C)))) * (-sqrt(2.0) / B);
	} else {
		tmp = ((-0.5 * sqrt(((1.0 / F) / t_0))) * ((C * sqrt(2.0)) * (B * (((F / (B * B)) * (1.0 + (A * sqrt((1.0 / fma(A, A, (B * B))))))) + (4.0 * ((A / pow(B, 4.0)) * t_1)))))) - ((sqrt(2.0) / B) * sqrt(t_1));
	}
	return tmp;
}

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(A - hypot(A, B))
	t_1 = Float64(F * t_0)
	tmp = 0.0
	if (B <= -28032165908107884.0)
		tmp = Float64(sqrt(Float64(F * Float64(C - hypot(C, B)))) / Float64(B / sqrt(2.0)));
	elseif (B <= 2.15e-135)
		tmp = Float64(-Float64(sqrt(Float64(-16.0 * Float64(Float64(C * A) * Float64(F * A)))) / Float64(Float64(B * B) + Float64(Float64(C * A) * -4.0))));
	elseif (B <= 1.55e+100)
		tmp = Float64(sqrt(Float64(F * Float64(Float64(B * B) * Float64(-0.5 / C)))) * Float64(Float64(-sqrt(2.0)) / B));
	else
		tmp = Float64(Float64(Float64(-0.5 * sqrt(Float64(Float64(1.0 / F) / t_0))) * Float64(Float64(C * sqrt(2.0)) * Float64(B * Float64(Float64(Float64(F / Float64(B * B)) * Float64(1.0 + Float64(A * sqrt(Float64(1.0 / fma(A, A, Float64(B * B))))))) + Float64(4.0 * Float64(Float64(A / (B ^ 4.0)) * t_1)))))) - Float64(Float64(sqrt(2.0) / B) * sqrt(t_1)));
	end
	return tmp
end

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[(A - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(F * t$95$0), $MachinePrecision]}, If[LessEqual[B, -28032165908107884.0], N[(N[Sqrt[N[(F * N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(B / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.15e-135], (-N[(N[Sqrt[N[(-16.0 * N[(N[(C * A), $MachinePrecision] * N[(F * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(N[(B * B), $MachinePrecision] + N[(N[(C * A), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[B, 1.55e+100], N[(N[Sqrt[N[(F * N[(N[(B * B), $MachinePrecision] * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[((-N[Sqrt[2.0], $MachinePrecision]) / B), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-0.5 * N[Sqrt[N[(N[(1.0 / F), $MachinePrecision] / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(C * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[(B * N[(N[(N[(F / N[(B * B), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(A * N[Sqrt[N[(1.0 / N[(A * A + N[(B * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(N[(A / N[Power[B, 4.0], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[Sqrt[2.0], $MachinePrecision] / B), $MachinePrecision] * N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

\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 := A - \mathsf{hypot}\left(A, B\right)\\
t_1 := F \cdot t_0\\
\mathbf{if}\;B \leq -28032165908107884:\\
\;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\

\mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\
\;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\

\mathbf{elif}\;B \leq 1.55 \cdot 10^{+100}:\\
\;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot \frac{-\sqrt{2}}{B}\\

\mathbf{else}:\\
\;\;\;\;\left(-0.5 \cdot \sqrt{\frac{\frac{1}{F}}{t_0}}\right) \cdot \left(\left(C \cdot \sqrt{2}\right) \cdot \left(B \cdot \left(\frac{F}{B \cdot B} \cdot \left(1 + A \cdot \sqrt{\frac{1}{\mathsf{fma}\left(A, A, B \cdot B\right)}}\right) + 4 \cdot \left(\frac{A}{{B}^{4}} \cdot t_1\right)\right)\right)\right) - \frac{\sqrt{2}}{B} \cdot \sqrt{t_1}\\


\end{array}

Error

Derivation

  1. Split input into 4 regimes

  2. if B < -28032165908107884

    1. Initial program 55.7

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

    2. Simplified57.9

      \[\leadsto \color{blue}{\frac{-\sqrt{F \cdot \left(2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C -4))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C)))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 22 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 A C) (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 18 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= sub-neg_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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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<= associate-*l*_binary64 (*.f64 (*.f64 F (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 5 points increase in error, 7 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite<= --rgt-identity_binary64 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> div-sub_binary64 (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (-.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)))))) 0) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (Rewrite=> --rgt-identity_binary64 (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 points increase in error, 0 points decrease in error
      (Rewrite<= div-sub_binary64 (/.f64 (-.f64 0 (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 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-sub0_binary64 (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 points increase in error, 0 points decrease in error

    3. Taylor expanded in A around 0 56.8

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

    4. Simplified56.5

      \[\leadsto \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof
      (*.f64 (*.f64 2 (-.f64 C (hypot.f64 B C))) (*.f64 F (*.f64 B B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C)))))) (*.f64 F (*.f64 B B))): 47 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C))))) (*.f64 F (*.f64 B B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2)))))) (*.f64 F (*.f64 B B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))))) (*.f64 F (Rewrite<= unpow2_binary64 (pow.f64 B 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (*.f64 F (pow.f64 B 2))))): 0 points increase in error, 0 points decrease in error

    5. Taylor expanded in A around 0 63.5

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

    6. Simplified62.4

      \[\leadsto \color{blue}{\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}\right)} \]
      Proof
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 B C)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C))))))))): 96 points increase in error, 2 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2))))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) F))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) F))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) F))))): 0 points increase in error, 0 points decrease in error

    7. Applied egg-rr36.8

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

    if -28032165908107884 < B < 2.14999999999999999e-135

    1. Initial program 50.4

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

    2. Simplified45.8

      \[\leadsto \color{blue}{\frac{-\sqrt{F \cdot \left(2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C -4))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C)))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 22 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 A C) (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 18 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= sub-neg_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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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<= associate-*l*_binary64 (*.f64 (*.f64 F (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 5 points increase in error, 7 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite<= --rgt-identity_binary64 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> div-sub_binary64 (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (-.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)))))) 0) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (Rewrite=> --rgt-identity_binary64 (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 points increase in error, 0 points decrease in error
      (Rewrite<= div-sub_binary64 (/.f64 (-.f64 0 (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 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-sub0_binary64 (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 points increase in error, 0 points decrease in error

    3. Taylor expanded in A around -inf 47.0

      \[\leadsto \frac{-\sqrt{\color{blue}{-16 \cdot \left({A}^{2} \cdot \left(C \cdot F\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

    4. Simplified47.0

      \[\leadsto \frac{-\sqrt{\color{blue}{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof
      (*.f64 -16 (*.f64 (*.f64 A A) (*.f64 F C))): 0 points increase in error, 0 points decrease in error
      (*.f64 -16 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 A 2)) (*.f64 F C))): 0 points increase in error, 0 points decrease in error
      (*.f64 -16 (*.f64 (pow.f64 A 2) (Rewrite<= *-commutative_binary64 (*.f64 C F)))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr37.2

      \[\leadsto \frac{-\sqrt{-16 \cdot \color{blue}{\left(0 + A \cdot \left(\left(A \cdot C\right) \cdot F\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

    6. Taylor expanded in A around 0 47.0

      \[\leadsto \frac{-\sqrt{-16 \cdot \left(0 + \color{blue}{{A}^{2} \cdot \left(C \cdot F\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]

    7. Simplified37.5

      \[\leadsto \frac{-\sqrt{-16 \cdot \left(0 + \color{blue}{\left(A \cdot C\right) \cdot \left(A \cdot F\right)}\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof
      (*.f64 (*.f64 A C) (*.f64 A F)): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 A C) (Rewrite<= *-commutative_binary64 (*.f64 F A))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 A C) F) A)): 23 points increase in error, 24 points decrease in error
      (*.f64 (Rewrite<= associate-*r*_binary64 (*.f64 A (*.f64 C F))) A): 25 points increase in error, 23 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 A (*.f64 A (*.f64 C F)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A A) (*.f64 C F))): 39 points increase in error, 10 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 A 2)) (*.f64 C F)): 0 points increase in error, 0 points decrease in error

    8. Applied egg-rr37.4

      \[\leadsto \frac{-\sqrt{-16 \cdot \left(0 + \left(A \cdot C\right) \cdot \left(A \cdot F\right)\right)}}{\color{blue}{B \cdot B + -4 \cdot \left(A \cdot C\right)}} \]

    if 2.14999999999999999e-135 < B < 1.55000000000000003e100

    1. Initial program 44.6

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

    2. Simplified41.7

      \[\leadsto \color{blue}{\frac{-\sqrt{F \cdot \left(2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C -4))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C)))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 22 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 A C) (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 18 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= sub-neg_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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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<= associate-*l*_binary64 (*.f64 (*.f64 F (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 5 points increase in error, 7 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite<= --rgt-identity_binary64 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> div-sub_binary64 (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (-.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)))))) 0) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (Rewrite=> --rgt-identity_binary64 (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 points increase in error, 0 points decrease in error
      (Rewrite<= div-sub_binary64 (/.f64 (-.f64 0 (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 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-sub0_binary64 (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 points increase in error, 0 points decrease in error

    3. Taylor expanded in A around 0 51.3

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

    4. Simplified50.7

      \[\leadsto \frac{-\sqrt{\color{blue}{\left(2 \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right) \cdot \left(F \cdot \left(B \cdot B\right)\right)}}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)} \]
      Proof
      (*.f64 (*.f64 2 (-.f64 C (hypot.f64 B C))) (*.f64 F (*.f64 B B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C)))))) (*.f64 F (*.f64 B B))): 47 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C))))) (*.f64 F (*.f64 B B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2)))))) (*.f64 F (*.f64 B B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 2 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))))) (*.f64 F (Rewrite<= unpow2_binary64 (pow.f64 B 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) (*.f64 F (pow.f64 B 2))))): 0 points increase in error, 0 points decrease in error

    5. Taylor expanded in A around 0 48.9

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

    6. Simplified48.2

      \[\leadsto \color{blue}{\frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)}\right)} \]
      Proof
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 B C)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 C C))))))))): 96 points increase in error, 2 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 C C)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (*.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 C 2))))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) F))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) F))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))) F))))): 0 points increase in error, 0 points decrease in error

    7. Taylor expanded in C around inf 46.7

      \[\leadsto \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \color{blue}{\left(-0.5 \cdot \frac{{B}^{2}}{C}\right)}}\right) \]

    8. Simplified46.7

      \[\leadsto \frac{\sqrt{2}}{B} \cdot \left(-\sqrt{F \cdot \color{blue}{\left(\frac{-0.5}{C} \cdot \left(B \cdot B\right)\right)}}\right) \]
      Proof
      (*.f64 (/.f64 -1/2 C) (*.f64 B B)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 -1/2 C) (Rewrite<= unpow2_binary64 (pow.f64 B 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 -1/2 (/.f64 C (pow.f64 B 2)))): 23 points increase in error, 14 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -1/2 (pow.f64 B 2)) C)): 12 points increase in error, 11 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -1/2 (/.f64 (pow.f64 B 2) C))): 1 points increase in error, 0 points decrease in error

    if 1.55000000000000003e100 < B

    1. Initial program 60.3

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

    2. Simplified63.8

      \[\leadsto \color{blue}{\frac{-\sqrt{F \cdot \left(2 \cdot \left(\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right) \cdot \left(A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}} \]
      Proof
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C -4))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C))))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C)))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.f64 A C)))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 22 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (-.f64 C (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (+.f64 A (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 A C) (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 18 points increase in error, 5 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) (Rewrite<= sub-neg_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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 F (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (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<= associate-*l*_binary64 (*.f64 (*.f64 F (*.f64 2 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 5 points increase in error, 7 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (sqrt.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.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 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite<= --rgt-identity_binary64 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.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)))))) 0))) (fma.f64 B B (*.f64 A (*.f64 C -4)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (*.f64 A (*.f64 C (Rewrite<= metadata-eval (neg.f64 4)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 A C) (neg.f64 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 A C) 4))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 A C)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (fma.f64 B B (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 0 (-.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)))))) 0)) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (*.f64 4 A) C))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> div-sub_binary64 (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (-.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)))))) 0) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 0 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) (/.f64 (Rewrite=> --rgt-identity_binary64 (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 points increase in error, 0 points decrease in error
      (Rewrite<= div-sub_binary64 (/.f64 (-.f64 0 (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 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-sub0_binary64 (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 points increase in error, 0 points decrease in error

    3. Taylor expanded in C around 0 57.3

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

    4. Simplified32.5

      \[\leadsto \color{blue}{\left(-0.5 \cdot \sqrt{\frac{\frac{1}{F}}{A - \mathsf{hypot}\left(A, B\right)}}\right) \cdot \left(\left(\sqrt{2} \cdot C\right) \cdot \left(B \cdot \left(\frac{F}{B \cdot B} \cdot \left(1 + A \cdot \sqrt{\frac{1}{\mathsf{fma}\left(A, A, B \cdot B\right)}}\right) + 4 \cdot \left(\frac{A}{{B}^{4}} \cdot \left(F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)\right)\right)\right)\right)\right) - \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)}} \]
      Proof
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (hypot.f64 A B))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 A A) (*.f64 B B)))))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 1 points increase in error, 3 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 A 2)) (*.f64 B B))))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (Rewrite<= unpow2_binary64 (pow.f64 B 2)))))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (Rewrite<= associate-/r*_binary64 (/.f64 1 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2))))))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (*.f64 B B)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (Rewrite<= unpow2_binary64 (pow.f64 B 2))) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 B B))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (fma.f64 A A (Rewrite<= unpow2_binary64 (pow.f64 B 2)))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 A A) (pow.f64 B 2)))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 A 2)) (pow.f64 B 2))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (+.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (+.f64 1 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2))))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (+.f64 1 (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (*.f64 (/.f64 F (pow.f64 B 2)) (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2))))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 F (/.f64 (pow.f64 B 2) (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2))) (*.f64 4 (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -4)) (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (hypot.f64 A B))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 A A) (*.f64 B B)))))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 46 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 A 2)) (*.f64 B B))))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (Rewrite<= unpow2_binary64 (pow.f64 B 2)))))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (*.f64 (/.f64 A (pow.f64 B 4)) (*.f64 F (-.f64 A (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (*.f64 (/.f64 A (pow.f64 B 4)) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (Rewrite<= associate-/r/_binary64 (/.f64 A (/.f64 (pow.f64 B 4) (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 2 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (+.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 (neg.f64 -4) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 4 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (*.f64 B (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 (*.f64 (sqrt.f64 2) C) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B)))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (Rewrite<= associate-*r*_binary64 (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 5 points increase in error, 1 points decrease in error
      (-.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B)))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 A A) (*.f64 B B))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 A 2)) (*.f64 B B)))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (Rewrite<= unpow2_binary64 (pow.f64 B 2))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 B 2) (pow.f64 A 2))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)))) (*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F))) (*.f64 (sqrt.f64 2) (*.f64 C (*.f64 (-.f64 (/.f64 (*.f64 F (-.f64 1 (*.f64 -1 (*.f64 A (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))))))) (pow.f64 B 2)) (*.f64 -4 (/.f64 (*.f64 A (*.f64 (-.f64 A (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 A 2)))) F)) (pow.f64 B 4)))) B))))))): 0 points increase in error, 0 points decrease in error
  3. Recombined 4 regimes into one program.

  4. Final simplification38.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot \frac{-\sqrt{2}}{B}\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot \sqrt{\frac{\frac{1}{F}}{A - \mathsf{hypot}\left(A, B\right)}}\right) \cdot \left(\left(C \cdot \sqrt{2}\right) \cdot \left(B \cdot \left(\frac{F}{B \cdot B} \cdot \left(1 + A \cdot \sqrt{\frac{1}{\mathsf{fma}\left(A, A, B \cdot B\right)}}\right) + 4 \cdot \left(\frac{A}{{B}^{4}} \cdot \left(F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)\right)\right)\right)\right)\right) - \frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(A - \mathsf{hypot}\left(A, B\right)\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error38.9
Cost20300
\[\begin{array}{l} t_0 := \sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}\\ \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{t_0}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot \frac{-\sqrt{2}}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 \cdot \sqrt{2}}{-B}\\ \end{array} \]
Alternative 2
Error38.9
Cost20300
\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)} \cdot t_0\\ \end{array} \]
Alternative 3
Error38.2
Cost20300
\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{F \cdot \left(A - \mathsf{hypot}\left(B, A\right)\right)} \cdot t_0\\ \end{array} \]
Alternative 4
Error38.9
Cost19972
\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)} \cdot \sqrt{2}}{B}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{B \cdot \left(-F\right)} \cdot t_0\\ \end{array} \]
Alternative 5
Error38.9
Cost19972
\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -28032165908107884:\\ \;\;\;\;\frac{\sqrt{F \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)}}{\frac{B}{\sqrt{2}}}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{B \cdot \left(-F\right)} \cdot t_0\\ \end{array} \]
Alternative 6
Error43.8
Cost14212
\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq -85000000000:\\ \;\;\;\;\frac{-\sqrt{2 \cdot \left(\left(F \cdot \left(B \cdot B\right)\right) \cdot \left(B + C\right)\right)}}{\mathsf{fma}\left(B, B, A \cdot \left(C \cdot -4\right)\right)}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;-\frac{\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B + \left(C \cdot A\right) \cdot -4}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{B \cdot \left(-F\right)} \cdot t_0\\ \end{array} \]
Alternative 7
Error43.8
Cost13960
\[\begin{array}{l} t_0 := \frac{-\sqrt{2}}{B}\\ \mathbf{if}\;B \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{F \cdot \left(\left(B \cdot B\right) \cdot \frac{-0.5}{C}\right)} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{B \cdot \left(-F\right)} \cdot t_0\\ \end{array} \]
Alternative 8
Error43.2
Cost13508
\[\begin{array}{l} \mathbf{if}\;B \leq 8 \cdot 10^{+54}:\\ \;\;\;\;\frac{-\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{A \cdot \left(C \cdot -4\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{B \cdot \left(-F\right)} \cdot \frac{-\sqrt{2}}{B}\\ \end{array} \]
Alternative 9
Error53.5
Cost7424
\[\frac{-\sqrt{-16 \cdot \left(\left(A \cdot A\right) \cdot \left(F \cdot C\right)\right)}}{A \cdot \left(C \cdot -4\right)} \]
Alternative 10
Error47.6
Cost7424
\[\frac{-\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{A \cdot \left(C \cdot -4\right)} \]
Alternative 11
Error62.7
Cost7296
\[\frac{-\sqrt{-16 \cdot \left(C \cdot \left(A \cdot \left(F \cdot A\right)\right)\right)}}{B \cdot B} \]
Alternative 12
Error62.7
Cost7296
\[\frac{-\sqrt{-16 \cdot \left(\left(C \cdot A\right) \cdot \left(F \cdot A\right)\right)}}{B \cdot B} \]

Error

Reproduce

herbie shell --seed 2022294 
(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))))