Average Error: 33.9 → 8.2
Time: 15.0s
Precision: binary64
Cost: 26892
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+102}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-207}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a \cdot 2}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\left(b - \mathsf{hypot}\left(\sqrt[3]{a} \cdot \sqrt{\sqrt[3]{a} \cdot \left(c \cdot -4\right)}, b\right)\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
↓
(FPCore (a b c)
 :precision binary64
 (if (<= b -9e+102)
   (/ (- b) a)
   (if (<= b -3.1e-207)
     (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
     (if (<= b 3e-72)
       (*
        (- b (hypot (* (cbrt a) (sqrt (* (cbrt a) (* c -4.0)))) b))
        (/ -0.5 a))
       (/ (- c) b)))))
double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}
↓
double code(double a, double b, double c) {
	double tmp;
	if (b <= -9e+102) {
		tmp = -b / a;
	} else if (b <= -3.1e-207) {
		tmp = (sqrt(((b * b) - (4.0 * (a * c)))) - b) / (a * 2.0);
	} else if (b <= 3e-72) {
		tmp = (b - hypot((cbrt(a) * sqrt((cbrt(a) * (c * -4.0)))), b)) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}
↓
public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -9e+102) {
		tmp = -b / a;
	} else if (b <= -3.1e-207) {
		tmp = (Math.sqrt(((b * b) - (4.0 * (a * c)))) - b) / (a * 2.0);
	} else if (b <= 3e-72) {
		tmp = (b - Math.hypot((Math.cbrt(a) * Math.sqrt((Math.cbrt(a) * (c * -4.0)))), b)) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end
↓
function code(a, b, c)
	tmp = 0.0
	if (b <= -9e+102)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= -3.1e-207)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c)))) - b) / Float64(a * 2.0));
	elseif (b <= 3e-72)
		tmp = Float64(Float64(b - hypot(Float64(cbrt(a) * sqrt(Float64(cbrt(a) * Float64(c * -4.0)))), b)) * Float64(-0.5 / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]
↓
code[a_, b_, c_] := If[LessEqual[b, -9e+102], N[((-b) / a), $MachinePrecision], If[LessEqual[b, -3.1e-207], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-72], N[(N[(b - N[Sqrt[N[(N[Power[a, 1/3], $MachinePrecision] * N[Sqrt[N[(N[Power[a, 1/3], $MachinePrecision] * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + b ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]]

\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \leq -9 \cdot 10^{+102}:\\
\;\;\;\;\frac{-b}{a}\\

\mathbf{elif}\;b \leq -3.1 \cdot 10^{-207}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a \cdot 2}\\

\mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\
\;\;\;\;\left(b - \mathsf{hypot}\left(\sqrt[3]{a} \cdot \sqrt{\sqrt[3]{a} \cdot \left(c \cdot -4\right)}, b\right)\right) \cdot \frac{-0.5}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{-c}{b}\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.9
Target20.8
Herbie8.2
\[\begin{array}{l} \mathbf{if}\;b < 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array} \]

Derivation

  1. Split input into 4 regimes

  2. if b < -9.00000000000000042e102

    1. Initial program 47.0

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

    2. Taylor expanded in b around -inf 3.2

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]

    3. Simplified3.2

      \[\leadsto \color{blue}{-\frac{b}{a}} \]
      Proof
      (neg.f64 (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 b a))): 0 points increase in error, 0 points decrease in error

    if -9.00000000000000042e102 < b < -3.1000000000000001e-207

    1. Initial program 7.5

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

    if -3.1000000000000001e-207 < b < 3e-72

    1. Initial program 19.0

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

    2. Simplified19.0

      \[\leadsto \color{blue}{\left(b - \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}\right) \cdot \frac{-0.5}{a}} \]
      Proof
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c (Rewrite<= metadata-eval (neg.f64 4))))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 a c) (neg.f64 4)))))) (/.f64 -1/2 a)): 0 points increase in error, 1 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 a c) 4)))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 a c))))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) 1)) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (Rewrite<= metadata-eval (neg.f64 -1))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (neg.f64 -1)) (/.f64 (Rewrite<= metadata-eval (/.f64 -1 2)) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (Rewrite=> metadata-eval 1)) (/.f64 (/.f64 -1 2) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite=> /-rgt-identity_binary64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (/.f64 (/.f64 -1 2) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (Rewrite<= associate-/r*_binary64 (/.f64 -1 (*.f64 2 a)))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) -1) (*.f64 2 a))): 10 points increase in error, 27 points decrease in error
      (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 b)) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error

    3. Applied egg-rr19.0

      \[\leadsto \left(b - \sqrt{\color{blue}{b \cdot b + a \cdot \left(c \cdot -4\right)}}\right) \cdot \frac{-0.5}{a} \]

    4. Applied egg-rr19.3

      \[\leadsto \left(b - \sqrt{\color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{a}\right)}^{2}, \sqrt[3]{a} \cdot \left(c \cdot -4\right), b \cdot b\right)}}\right) \cdot \frac{-0.5}{a} \]

    5. Applied egg-rr11.5

      \[\leadsto \left(b - \color{blue}{\mathsf{hypot}\left(\sqrt[3]{a} \cdot \sqrt{\sqrt[3]{a} \cdot \left(c \cdot -4\right)}, b\right)}\right) \cdot \frac{-0.5}{a} \]

    if 3e-72 < b

    1. Initial program 53.4

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

    2. Simplified53.4

      \[\leadsto \color{blue}{\left(b - \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}\right) \cdot \frac{-0.5}{a}} \]
      Proof
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c (Rewrite<= metadata-eval (neg.f64 4))))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 a c) (neg.f64 4)))))) (/.f64 -1/2 a)): 0 points increase in error, 1 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 a c) 4)))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 a c))))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) 1)) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (Rewrite<= metadata-eval (neg.f64 -1))) (/.f64 -1/2 a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (neg.f64 -1)) (/.f64 (Rewrite<= metadata-eval (/.f64 -1 2)) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (Rewrite=> metadata-eval 1)) (/.f64 (/.f64 -1 2) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite=> /-rgt-identity_binary64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (/.f64 (/.f64 -1 2) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (Rewrite<= associate-/r*_binary64 (/.f64 -1 (*.f64 2 a)))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) -1) (*.f64 2 a))): 10 points increase in error, 27 points decrease in error
      (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 b)) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a)): 0 points increase in error, 0 points decrease in error

    3. Taylor expanded in b around inf 19.8

      \[\leadsto \color{blue}{\left(2 \cdot \frac{c \cdot a}{b}\right)} \cdot \frac{-0.5}{a} \]

    4. Simplified19.9

      \[\leadsto \color{blue}{\left(\frac{2}{b} \cdot \left(c \cdot a\right)\right)} \cdot \frac{-0.5}{a} \]
      Proof
      (*.f64 (/.f64 2 b) (*.f64 c a)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 b (*.f64 c a)))): 33 points increase in error, 34 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 2 (*.f64 c a)) b)): 25 points increase in error, 25 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 2 (/.f64 (*.f64 c a) b))): 1 points increase in error, 2 points decrease in error

    5. Taylor expanded in b around 0 8.8

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}} \]

    6. Simplified8.8

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

  4. Final simplification8.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+102}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-207}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a \cdot 2}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\left(b - \mathsf{hypot}\left(\sqrt[3]{a} \cdot \sqrt{\sqrt[3]{a} \cdot \left(c \cdot -4\right)}, b\right)\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternatives

Alternative 1
Error10.1
Cost7624
\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{b \cdot b + a \cdot \left(c \cdot -4\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 2
Error9.8
Cost7624
\[\begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+102}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 3
Error13.1
Cost7368
\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{c \cdot \left(a \cdot -4\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 4
Error13.0
Cost7368
\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 5
Error22.7
Cost388
\[\begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-277}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 6
Error40.0
Cost256
\[\frac{-c}{b} \]
Alternative 7
Error56.7
Cost192
\[\frac{c}{b} \]

Error

Reproduce

herbie shell --seed 2022308 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64

  :herbie-target
  (if (< b 0.0) (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)) (/ c (* a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))))

  (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))