Average Error: 34.0 → 10.1
Time: 6.0s
Precision: binary64
\[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a} \]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \leq -1 \cdot 10^{+150}:\\ \;\;\;\;\frac{b_2}{a} \cdot -2\\ \mathbf{elif}\;b_2 \leq 1.45 \cdot 10^{-118}:\\ \;\;\;\;\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \end{array} \]
(FPCore (a b_2 c)
 :precision binary64
 (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
↓
(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1e+150)
   (* (/ b_2 a) -2.0)
   (if (<= b_2 1.45e-118)
     (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
     (/ (* c -0.5) b_2))))
double code(double a, double b_2, double c) {
	return (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a;
}
↓
double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1e+150) {
		tmp = (b_2 / a) * -2.0;
	} else if (b_2 <= 1.45e-118) {
		tmp = (sqrt(((b_2 * b_2) - (a * c))) - b_2) / a;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a
end function
↓
real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-1d+150)) then
        tmp = (b_2 / a) * (-2.0d0)
    else if (b_2 <= 1.45d-118) then
        tmp = (sqrt(((b_2 * b_2) - (a * c))) - b_2) / a
    else
        tmp = (c * (-0.5d0)) / b_2
    end if
    code = tmp
end function

public static double code(double a, double b_2, double c) {
	return (-b_2 + Math.sqrt(((b_2 * b_2) - (a * c)))) / a;
}
↓
public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1e+150) {
		tmp = (b_2 / a) * -2.0;
	} else if (b_2 <= 1.45e-118) {
		tmp = (Math.sqrt(((b_2 * b_2) - (a * c))) - b_2) / a;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

def code(a, b_2, c):
	return (-b_2 + math.sqrt(((b_2 * b_2) - (a * c)))) / a
↓
def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1e+150:
		tmp = (b_2 / a) * -2.0
	elif b_2 <= 1.45e-118:
		tmp = (math.sqrt(((b_2 * b_2) - (a * c))) - b_2) / a
	else:
		tmp = (c * -0.5) / b_2
	return tmp

function code(a, b_2, c)
	return Float64(Float64(Float64(-b_2) + sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c)))) / a)
end
↓
function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1e+150)
		tmp = Float64(Float64(b_2 / a) * -2.0);
	elseif (b_2 <= 1.45e-118)
		tmp = Float64(Float64(sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c))) - b_2) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b_2);
	end
	return tmp
end

function tmp = code(a, b_2, c)
	tmp = (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a;
end
↓
function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1e+150)
		tmp = (b_2 / a) * -2.0;
	elseif (b_2 <= 1.45e-118)
		tmp = (sqrt(((b_2 * b_2) - (a * c))) - b_2) / a;
	else
		tmp = (c * -0.5) / b_2;
	end
	tmp_2 = tmp;
end

code[a_, b$95$2_, c_] := N[(N[((-b$95$2) + N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]
↓
code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1e+150], N[(N[(b$95$2 / a), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[b$95$2, 1.45e-118], N[(N[(N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b$95$2), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision]]]

\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}
↓
\begin{array}{l}
\mathbf{if}\;b_2 \leq -1 \cdot 10^{+150}:\\
\;\;\;\;\frac{b_2}{a} \cdot -2\\

\mathbf{elif}\;b_2 \leq 1.45 \cdot 10^{-118}:\\
\;\;\;\;\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{c \cdot -0.5}{b_2}\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if b_2 < -9.99999999999999981e149

    1. Initial program 62.0

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a} \]

    2. Simplified62.0

      \[\leadsto \color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}} \]

    3. Applied egg-rr62.0

      \[\leadsto \color{blue}{\left(\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2\right) \cdot \frac{1}{a}} \]

    4. Taylor expanded in b_2 around -inf 2.6

      \[\leadsto \color{blue}{-2 \cdot \frac{b_2}{a}} \]

    5. Simplified2.6

      \[\leadsto \color{blue}{\frac{b_2}{a} \cdot -2} \]

    if -9.99999999999999981e149 < b_2 < 1.4499999999999999e-118

    1. Initial program 11.0

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a} \]

    2. Simplified11.0

      \[\leadsto \color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}} \]

    if 1.4499999999999999e-118 < b_2

    1. Initial program 51.3

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a} \]

    2. Simplified51.3

      \[\leadsto \color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}} \]

    3. Applied egg-rr51.3

      \[\leadsto \color{blue}{{\left(\frac{a}{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}\right)}^{-1}} \]

    4. Taylor expanded in a around 0 11.2

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b_2}} \]

    5. Simplified11.2

      \[\leadsto \color{blue}{\frac{-0.5 \cdot c}{b_2}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \leq -1 \cdot 10^{+150}:\\ \;\;\;\;\frac{b_2}{a} \cdot -2\\ \mathbf{elif}\;b_2 \leq 1.45 \cdot 10^{-118}:\\ \;\;\;\;\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \end{array} \]

Reproduce

herbie shell --seed 2022192 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  :precision binary64
  (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))