quadp (p42, positive)

Average Accuracy: 47.2% → 78.0%

Time: 24.0s

Precision: binary64

Cost: 49680

Math

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

↓

\[\begin{array}{l} t_0 := \frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, -0.5 \cdot \frac{b}{c}\right)}\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-270}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{\mathsf{hypot}\left(b, \sqrt{c \cdot -4} \cdot \sqrt{a}\right) - b}}\\ \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

↓

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- (sqrt (+ (* b b) (* (* a c) -4.0))) b) (* a 2.0))))
   (if (<= t_0 (- INFINITY))
     (/ 0.5 (fma 0.5 (/ a b) (* -0.5 (/ b c))))
     (if (<= t_0 -1e-270)
       t_0
       (if (<= t_0 0.0)
         (- (/ c b))
         (if (<= t_0 5e+304)
           t_0
           (/ 0.5 (/ a (- (hypot b (* (sqrt (* c -4.0)) (sqrt a))) b)))))))))

C

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 t_0 = (sqrt(((b * b) + ((a * c) * -4.0))) - b) / (a * 2.0);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = 0.5 / fma(0.5, (a / b), (-0.5 * (b / c)));
	} else if (t_0 <= -1e-270) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = -(c / b);
	} else if (t_0 <= 5e+304) {
		tmp = t_0;
	} else {
		tmp = 0.5 / (a / (hypot(b, (sqrt((c * -4.0)) * sqrt(a))) - b));
	}
	return tmp;
}

Julia

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)
	t_0 = Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(Float64(a * c) * -4.0))) - b) / Float64(a * 2.0))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(0.5 / fma(0.5, Float64(a / b), Float64(-0.5 * Float64(b / c))));
	elseif (t_0 <= -1e-270)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(-Float64(c / b));
	elseif (t_0 <= 5e+304)
		tmp = t_0;
	else
		tmp = Float64(0.5 / Float64(a / Float64(hypot(b, Float64(sqrt(Float64(c * -4.0)) * sqrt(a))) - b)));
	end
	return tmp
end

Wolfram

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_] := Block[{t$95$0 = N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(N[(a * c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(0.5 / N[(0.5 * N[(a / b), $MachinePrecision] + N[(-0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -1e-270], t$95$0, If[LessEqual[t$95$0, 0.0], (-N[(c / b), $MachinePrecision]), If[LessEqual[t$95$0, 5e+304], t$95$0, N[(0.5 / N[(a / N[(N[Sqrt[b ^ 2 + N[(N[Sqrt[N[(c * -4.0), $MachinePrecision]], $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	47.2%
Target	67.7%
Herbie	78.0%

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a)) < -inf.0

   1. Initial program 0.0%

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

   2. Simplified 0.0%

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

      [Start] 0.0	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
      /-rgt-identity [<=] 0.0	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\color{blue}{\frac{2 \cdot a}{1}}} \]
      metadata-eval [<=] 0.0	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\frac{2 \cdot a}{\color{blue}{--1}}} \]
      *-commutative [=>] 0.0	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\frac{\color{blue}{a \cdot 2}}{--1}} \]
      associate-/l* [=>] 0.0	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\color{blue}{\frac{a}{\frac{--1}{2}}}} \]
      associate-/l* [<=] 0.0	\[ \color{blue}{\frac{\left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{--1}{2}}{a}} \]
      associate-*r/ [<=] 0.0	\[ \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{\frac{--1}{2}}{a}} \]
      /-rgt-identity [<=] 0.0	\[ \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{1}} \cdot \frac{\frac{--1}{2}}{a} \]
      metadata-eval [<=] 0.0	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\color{blue}{--1}} \cdot \frac{\frac{--1}{2}}{a} \]

   3. Applied egg-rr 26.2%

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

      [Start] 0.0	\[ \left(\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b\right) \cdot \frac{0.5}{a} \]
      associate-*r/ [=>] 0.0	\[ \color{blue}{\frac{\left(\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b\right) \cdot 0.5}{a}} \]
      *-commutative [=>] 0.0	\[ \frac{\color{blue}{0.5 \cdot \left(\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b\right)}}{a} \]
      associate-/l* [=>] 0.0	\[ \color{blue}{\frac{0.5}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b}}} \]
      fma-udef [=>] 0.0	\[ \frac{0.5}{\frac{a}{\sqrt{\color{blue}{b \cdot b + a \cdot \left(c \cdot -4\right)}} - b}} \]
      add-sqr-sqrt [=>] 0.0	\[ \frac{0.5}{\frac{a}{\sqrt{b \cdot b + \color{blue}{\sqrt{a \cdot \left(c \cdot -4\right)} \cdot \sqrt{a \cdot \left(c \cdot -4\right)}}} - b}} \]
      hypot-def [=>] 26.2	\[ \frac{0.5}{\frac{a}{\color{blue}{\mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -4\right)}\right)} - b}} \]

   4. Taylor expanded in b around inf 0.0%

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

   5. Simplified 48.4%

      \[\leadsto \frac{0.5}{\color{blue}{\mathsf{fma}\left(0.5, \frac{a}{b}, -0.5 \cdot \frac{b}{c}\right)}} \]
      Proof

      [Start] 0.0	\[ \frac{0.5}{2 \cdot \frac{b}{c \cdot {\left(\sqrt{-4}\right)}^{2}} + 0.5 \cdot \frac{a}{b}} \]
      +-commutative [=>] 0.0	\[ \frac{0.5}{\color{blue}{0.5 \cdot \frac{a}{b} + 2 \cdot \frac{b}{c \cdot {\left(\sqrt{-4}\right)}^{2}}}} \]
      fma-def [=>] 0.0	\[ \frac{0.5}{\color{blue}{\mathsf{fma}\left(0.5, \frac{a}{b}, 2 \cdot \frac{b}{c \cdot {\left(\sqrt{-4}\right)}^{2}}\right)}} \]
      associate-*r/ [=>] 0.0	\[ \frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, \color{blue}{\frac{2 \cdot b}{c \cdot {\left(\sqrt{-4}\right)}^{2}}}\right)} \]
      *-commutative [=>] 0.0	\[ \frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, \frac{2 \cdot b}{\color{blue}{{\left(\sqrt{-4}\right)}^{2} \cdot c}}\right)} \]
      times-frac [=>] 0.0	\[ \frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, \color{blue}{\frac{2}{{\left(\sqrt{-4}\right)}^{2}} \cdot \frac{b}{c}}\right)} \]
      unpow2 [=>] 0.0	\[ \frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, \frac{2}{\color{blue}{\sqrt{-4} \cdot \sqrt{-4}}} \cdot \frac{b}{c}\right)} \]
      rem-square-sqrt [=>] 48.4	\[ \frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, \frac{2}{\color{blue}{-4}} \cdot \frac{b}{c}\right)} \]
      metadata-eval [=>] 48.4	\[ \frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, \color{blue}{-0.5} \cdot \frac{b}{c}\right)} \]

   if -inf.0 < (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a)) < -1e-270 or 0.0 < (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a)) < 4.9999999999999997e304

   1. Initial program 94.2%

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

   if -1e-270 < (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a)) < 0.0

   1. Initial program 17.2%

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

   2. Taylor expanded in b around inf 99.3%

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

   3. Simplified 99.3%

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

      [Start] 99.3	\[ -1 \cdot \frac{c}{b} \]
      associate-*r/ [=>] 99.3	\[ \color{blue}{\frac{-1 \cdot c}{b}} \]
      neg-mul-1 [<=] 99.3	\[ \frac{\color{blue}{-c}}{b} \]

   if 4.9999999999999997e304 < (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))

   1. Initial program 0.3%

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

   2. Simplified 0.3%

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

      [Start] 0.3	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
      /-rgt-identity [<=] 0.3	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\color{blue}{\frac{2 \cdot a}{1}}} \]
      metadata-eval [<=] 0.3	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\frac{2 \cdot a}{\color{blue}{--1}}} \]
      *-commutative [=>] 0.3	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\frac{\color{blue}{a \cdot 2}}{--1}} \]
      associate-/l* [=>] 0.3	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\color{blue}{\frac{a}{\frac{--1}{2}}}} \]
      associate-/l* [<=] 0.3	\[ \color{blue}{\frac{\left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{--1}{2}}{a}} \]
      associate-*r/ [<=] 0.3	\[ \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{\frac{--1}{2}}{a}} \]
      /-rgt-identity [<=] 0.3	\[ \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{1}} \cdot \frac{\frac{--1}{2}}{a} \]
      metadata-eval [<=] 0.3	\[ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\color{blue}{--1}} \cdot \frac{\frac{--1}{2}}{a} \]

   3. Applied egg-rr 24.0%

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

      [Start] 0.3	\[ \left(\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b\right) \cdot \frac{0.5}{a} \]
      associate-*r/ [=>] 0.3	\[ \color{blue}{\frac{\left(\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b\right) \cdot 0.5}{a}} \]
      *-commutative [=>] 0.3	\[ \frac{\color{blue}{0.5 \cdot \left(\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b\right)}}{a} \]
      associate-/l* [=>] 0.3	\[ \color{blue}{\frac{0.5}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)} - b}}} \]
      fma-udef [=>] 0.3	\[ \frac{0.5}{\frac{a}{\sqrt{\color{blue}{b \cdot b + a \cdot \left(c \cdot -4\right)}} - b}} \]
      add-sqr-sqrt [=>] 0.2	\[ \frac{0.5}{\frac{a}{\sqrt{b \cdot b + \color{blue}{\sqrt{a \cdot \left(c \cdot -4\right)} \cdot \sqrt{a \cdot \left(c \cdot -4\right)}}} - b}} \]
      hypot-def [=>] 24.0	\[ \frac{0.5}{\frac{a}{\color{blue}{\mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -4\right)}\right)} - b}} \]

   4. Applied egg-rr 44.4%

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

      [Start] 24.0	\[ \frac{0.5}{\frac{a}{\mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -4\right)}\right) - b}} \]
      sqrt-prod [=>] 44.4	\[ \frac{0.5}{\frac{a}{\mathsf{hypot}\left(b, \color{blue}{\sqrt{a} \cdot \sqrt{c \cdot -4}}\right) - b}} \]
      *-commutative [=>] 44.4	\[ \frac{0.5}{\frac{a}{\mathsf{hypot}\left(b, \color{blue}{\sqrt{c \cdot -4} \cdot \sqrt{a}}\right) - b}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2} \leq -\infty:\\ \;\;\;\;\frac{0.5}{\mathsf{fma}\left(0.5, \frac{a}{b}, -0.5 \cdot \frac{b}{c}\right)}\\ \mathbf{elif}\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2} \leq -1 \cdot 10^{-270}:\\ \;\;\;\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2}\\ \mathbf{elif}\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2} \leq 0:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{\mathsf{hypot}\left(b, \sqrt{c \cdot -4} \cdot \sqrt{a}\right) - b}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	84.0%
Cost	7624

\[\begin{array}{l} \mathbf{if}\;b \leq -1.58 \cdot 10^{+113}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-63}:\\ \;\;\;\;\left(\sqrt{b \cdot b + a \cdot \left(c \cdot -4\right)} - b\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array} \]

Alternative 2
Accuracy	84.1%
Cost	7624

\[\begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+120}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-60}:\\ \;\;\;\;\frac{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array} \]

Alternative 3
Accuracy	79.1%
Cost	7368

\[\begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-73}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(\sqrt{a \cdot \left(c \cdot -4\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array} \]

Alternative 4
Accuracy	79.0%
Cost	7368

\[\begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-65}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 10^{-61}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array} \]

Alternative 5
Accuracy	64.6%
Cost	580

\[\begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-294}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array} \]

Alternative 6
Accuracy	38.3%
Cost	388

\[\begin{array}{l} \mathbf{if}\;b \leq 0.155:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 7
Accuracy	64.6%
Cost	388

\[\begin{array}{l} \mathbf{if}\;b \leq 1.75 \cdot 10^{-281}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array} \]

Alternative 8
Accuracy	11.7%
Cost	192

\[\frac{c}{b} \]

Reproduce

herbie shell --seed 2023137 
(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)))