Average Error: 32.9 → 10.3
Time: 16.2s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -9.088000531423294 \cdot 10^{+152}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 9.354082991670835 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c}}{a}}{2} - \frac{\frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -9.088000531423294 \cdot 10^{+152}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 9.354082991670835 \cdot 10^{-125}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c}}{a}}{2} - \frac{\frac{b}{a}}{2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r1309299 = b;
        double r1309300 = -r1309299;
        double r1309301 = r1309299 * r1309299;
        double r1309302 = 4.0;
        double r1309303 = a;
        double r1309304 = c;
        double r1309305 = r1309303 * r1309304;
        double r1309306 = r1309302 * r1309305;
        double r1309307 = r1309301 - r1309306;
        double r1309308 = sqrt(r1309307);
        double r1309309 = r1309300 + r1309308;
        double r1309310 = 2.0;
        double r1309311 = r1309310 * r1309303;
        double r1309312 = r1309309 / r1309311;
        return r1309312;
}
↓
double f(double a, double b, double c) {
        double r1309313 = b;
        double r1309314 = -9.088000531423294e+152;
        bool r1309315 = r1309313 <= r1309314;
        double r1309316 = c;
        double r1309317 = r1309316 / r1309313;
        double r1309318 = a;
        double r1309319 = r1309313 / r1309318;
        double r1309320 = r1309317 - r1309319;
        double r1309321 = 9.354082991670835e-125;
        bool r1309322 = r1309313 <= r1309321;
        double r1309323 = r1309313 * r1309313;
        double r1309324 = 4.0;
        double r1309325 = r1309318 * r1309324;
        double r1309326 = r1309325 * r1309316;
        double r1309327 = r1309323 - r1309326;
        double r1309328 = sqrt(r1309327);
        double r1309329 = r1309328 / r1309318;
        double r1309330 = 2.0;
        double r1309331 = r1309329 / r1309330;
        double r1309332 = r1309319 / r1309330;
        double r1309333 = r1309331 - r1309332;
        double r1309334 = -r1309317;
        double r1309335 = r1309322 ? r1309333 : r1309334;
        double r1309336 = r1309315 ? r1309320 : r1309335;
        return r1309336;
}

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

Target

Original32.9
Target20.3
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -9.088000531423294e+152

    1. Initial program 60.4

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

    2. Simplified60.4

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

    3. Taylor expanded around -inf 1.5

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

    if -9.088000531423294e+152 < b < 9.354082991670835e-125

    1. Initial program 10.9

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

    2. Simplified10.9

      \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
    3. Using strategy rm

    4. Applied div-sub10.9

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

    5. Applied div-sub10.9

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

    if 9.354082991670835e-125 < b

    1. Initial program 49.8

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

    2. Simplified49.8

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

    3. Taylor expanded around inf 11.9

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

    4. Simplified11.9

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.088000531423294 \cdot 10^{+152}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 9.354082991670835 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c}}{a}}{2} - \frac{\frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (a b c)
  :name "quadp (p42, positive)"

  :herbie-target
  (if (< b 0) (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (/ c (* a (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))))

  (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))