Average Error: 19.6 → 8.5
Time: 5.8s
Precision: binary64
\[\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -1.3305907505166363 \cdot 10^{+154}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \leq 2.468062116429859 \cdot 10^{+148}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\ \end{array}\]
\begin{array}{l}
\mathbf{if}\;b \geq 0:\\
\;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

\end{array}
↓
\begin{array}{l}
\mathbf{if}\;b \leq -1.3305907505166363 \cdot 10^{+154}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \geq 0:\\
\;\;\;\;-2 \cdot \frac{c}{b + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) - b}{a \cdot 2}\\

\end{array}\\

\mathbf{elif}\;b \leq 2.468062116429859 \cdot 10^{+148}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \geq 0:\\
\;\;\;\;-2 \cdot \frac{c}{b + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\

\end{array}\\

\mathbf{elif}\;b \geq 0:\\
\;\;\;\;-2 \cdot \frac{c}{b + \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\

\end{array}
(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0)
   (/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))
↓
(FPCore (a b c)
 :precision binary64
 (if (<= b -1.3305907505166363e+154)
   (if (>= b 0.0)
     (* -2.0 (/ c (+ b (sqrt (- (* b b) (* c (* 4.0 a)))))))
     (/ (- (- (* 2.0 (/ (* c a) b)) b) b) (* a 2.0)))
   (if (<= b 2.468062116429859e+148)
     (if (>= b 0.0)
       (* -2.0 (/ c (+ b (sqrt (- (* b b) (* c (* 4.0 a)))))))
       (/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* a 2.0)))
     (if (>= b 0.0)
       (* -2.0 (/ c (+ b (- b (* 2.0 (/ (* c a) b))))))
       (/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* a 2.0))))))
double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = (2.0 * c) / (-b - sqrt((b * b) - ((4.0 * a) * c)));
	} else {
		tmp = (-b + sqrt((b * b) - ((4.0 * a) * c))) / (2.0 * a);
	}
	return tmp;
}
↓
double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.3305907505166363e+154) {
		double tmp_1;
		if (b >= 0.0) {
			tmp_1 = -2.0 * (c / (b + sqrt((b * b) - (c * (4.0 * a)))));
		} else {
			tmp_1 = (((2.0 * ((c * a) / b)) - b) - b) / (a * 2.0);
		}
		tmp = tmp_1;
	} else if (b <= 2.468062116429859e+148) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -2.0 * (c / (b + sqrt((b * b) - (c * (4.0 * a)))));
		} else {
			tmp_2 = (sqrt((b * b) - (c * (4.0 * a))) - b) / (a * 2.0);
		}
		tmp = tmp_2;
	} else if (b >= 0.0) {
		tmp = -2.0 * (c / (b + (b - (2.0 * ((c * a) / b)))));
	} else {
		tmp = (sqrt((b * b) - (c * (4.0 * a))) - b) / (a * 2.0);
	}
	return tmp;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if b < -1.330590750516636e154

    1. Initial program 64.0

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

    2. Simplified64.0

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

    3. Taylor expanded around -inf 12.5

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

    4. Simplified12.5

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

    if -1.330590750516636e154 < b < 2.468062116429859e148

    1. Initial program 8.4

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

    2. Simplified8.4

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

    if 2.468062116429859e148 < b

    1. Initial program 36.9

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

    2. Simplified36.9

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

    3. Taylor expanded around inf 6.7

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

    4. Simplified6.7

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{2 \cdot a}\\ \end{array}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification8.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3305907505166363 \cdot 10^{+154}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \leq 2.468062116429859 \cdot 10^{+148}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;-2 \cdot \frac{c}{b + \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(FPCore (a b c)
  :name "jeff quadratic root 2"
  :precision binary64
  (if (>= b 0.0) (/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))