Average Error: 33.7 → 10.4
Time: 16.1s
Precision: binary64
Cost: 7624
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+62}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\sqrt{b \cdot b + \left(c \cdot a\right) \cdot -4} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
(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 -1.65e+62)
   (- (/ c b) (/ b a))
   (if (<= b 6.5e-81)
     (/ (- (sqrt (+ (* b b) (* (* c a) -4.0))) b) (* a 2.0))
     (/ (- 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 <= -1.65e+62) {
		tmp = (c / b) - (b / a);
	} else if (b <= 6.5e-81) {
		tmp = (sqrt(((b * b) + ((c * a) * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function
↓
real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.65d+62)) then
        tmp = (c / b) - (b / a)
    else if (b <= 6.5d-81) then
        tmp = (sqrt(((b * b) + ((c * a) * (-4.0d0)))) - b) / (a * 2.0d0)
    else
        tmp = -c / b
    end if
    code = tmp
end function

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 <= -1.65e+62) {
		tmp = (c / b) - (b / a);
	} else if (b <= 6.5e-81) {
		tmp = (Math.sqrt(((b * b) + ((c * a) * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)
↓
def code(a, b, c):
	tmp = 0
	if b <= -1.65e+62:
		tmp = (c / b) - (b / a)
	elif b <= 6.5e-81:
		tmp = (math.sqrt(((b * b) + ((c * a) * -4.0))) - b) / (a * 2.0)
	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 <= -1.65e+62)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 6.5e-81)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(Float64(c * a) * -4.0))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end
↓
function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.65e+62)
		tmp = (c / b) - (b / a);
	elseif (b <= 6.5e-81)
		tmp = (sqrt(((b * b) + ((c * a) * -4.0))) - b) / (a * 2.0);
	else
		tmp = -c / b;
	end
	tmp_2 = 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, -1.65e+62], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-81], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(N[(c * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $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 -1.65 \cdot 10^{+62}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \leq 6.5 \cdot 10^{-81}:\\
\;\;\;\;\frac{\sqrt{b \cdot b + \left(c \cdot a\right) \cdot -4} - b}{a \cdot 2}\\

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


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.7
Target20.8
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;b < 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.65e62

    1. Initial program 39.7

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

    2. Simplified39.8

      \[\leadsto \color{blue}{\left(b - \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}\right) \cdot \frac{-0.5}{a}} \]
      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, 0 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, 1 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))): 6 points increase in error, 21 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-rr34.6

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(b - \mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -4\right)}\right)\right) \cdot -0.5}}} \]

    4. Applied egg-rr34.6

      \[\leadsto \frac{1}{\color{blue}{\frac{-2}{b - \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)} \cdot a}} \]

    5. Applied egg-rr34.7

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-2}{b - \mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -4\right)}\right)}}{\frac{1}{a}}}} \]

    6. Taylor expanded in b around -inf 64.0

      \[\leadsto \color{blue}{-0.25 \cdot \frac{c \cdot {\left(\sqrt{-4}\right)}^{2}}{b} + -1 \cdot \frac{b}{a}} \]

    7. Simplified5.3

      \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}} \]
      Proof
      (-.f64 (/.f64 c b) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 c)) b) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 -1/4 -4)) c) b) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 (*.f64 -1/4 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -4) (sqrt.f64 -4)))) c) b) (/.f64 b a)): 214 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 (*.f64 -1/4 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -4) 2))) c) b) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1/4 (*.f64 (pow.f64 (sqrt.f64 -4) 2) c))) b) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 -1/4 (Rewrite<= *-commutative_binary64 (*.f64 c (pow.f64 (sqrt.f64 -4) 2)))) b) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1/4 (/.f64 (*.f64 c (pow.f64 (sqrt.f64 -4) 2)) b))) (/.f64 b a)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/4 (/.f64 (*.f64 c (pow.f64 (sqrt.f64 -4) 2)) b)) (neg.f64 (/.f64 b a)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1/4 (/.f64 (*.f64 c (pow.f64 (sqrt.f64 -4) 2)) b)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 b a)))): 0 points increase in error, 0 points decrease in error

    if -1.65e62 < b < 6.5000000000000002e-81

    1. Initial program 13.2

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

    if 6.5000000000000002e-81 < b

    1. Initial program 52.4

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

    2. Simplified52.4

      \[\leadsto \color{blue}{\left(b - \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}\right) \cdot \frac{-0.5}{a}} \]
      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, 0 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, 1 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))): 6 points increase in error, 21 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 20.5

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

    4. Simplified17.5

      \[\leadsto \color{blue}{\left(\frac{2 \cdot c}{b} \cdot a\right)} \cdot \frac{-0.5}{a} \]
      Proof
      (*.f64 (/.f64 (*.f64 2 c) b) a): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 2 c) (/.f64 b a))): 45 points increase in error, 46 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 2 (/.f64 c (/.f64 b a)))): 1 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 c a) b))): 50 points increase in error, 44 points decrease in error

    5. Taylor expanded in c around 0 9.8

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

    6. Simplified9.8

      \[\leadsto \color{blue}{\frac{-c}{b}} \]
      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 3 regimes into one program.

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+62}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\sqrt{b \cdot b + \left(c \cdot a\right) \cdot -4} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternatives

Alternative 1
Error11.1
Cost7624
\[\begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;\left(b - \sqrt{b \cdot b + a \cdot \left(c \cdot -4\right)}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 2
Error13.9
Cost7368
\[\begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{-31}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{c \cdot \left(a \cdot -4\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 3
Error13.8
Cost7368
\[\begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{-31}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 4
Error22.9
Cost388
\[\begin{array}{l} \mathbf{if}\;b \leq 4.5 \cdot 10^{-244}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]
Alternative 5
Error40.0
Cost256
\[\frac{-c}{b} \]
Alternative 6
Error62.3
Cost192
\[\frac{b}{a} \]
Alternative 7
Error57.0
Cost192
\[\frac{c}{b} \]

Error

Reproduce

herbie shell --seed 2022312 
(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)))