Average Error: 33.3 → 9.7
Time: 15.4s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -5.7874989996849275 \cdot 10^{-40}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 1.7665622931893247 \cdot 10^{+83}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + c \cdot \left(-4 \cdot a\right)}}{a} \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -5.7874989996849275 \cdot 10^{-40}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 1.7665622931893247 \cdot 10^{+83}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + c \cdot \left(-4 \cdot a\right)}}{a} \cdot \frac{1}{2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r1441364 = b;
        double r1441365 = -r1441364;
        double r1441366 = r1441364 * r1441364;
        double r1441367 = 4.0;
        double r1441368 = a;
        double r1441369 = c;
        double r1441370 = r1441368 * r1441369;
        double r1441371 = r1441367 * r1441370;
        double r1441372 = r1441366 - r1441371;
        double r1441373 = sqrt(r1441372);
        double r1441374 = r1441365 - r1441373;
        double r1441375 = 2.0;
        double r1441376 = r1441375 * r1441368;
        double r1441377 = r1441374 / r1441376;
        return r1441377;
}
↓
double f(double a, double b, double c) {
        double r1441378 = b;
        double r1441379 = -5.7874989996849275e-40;
        bool r1441380 = r1441378 <= r1441379;
        double r1441381 = c;
        double r1441382 = r1441381 / r1441378;
        double r1441383 = -r1441382;
        double r1441384 = 1.7665622931893247e+83;
        bool r1441385 = r1441378 <= r1441384;
        double r1441386 = -r1441378;
        double r1441387 = r1441378 * r1441378;
        double r1441388 = -4.0;
        double r1441389 = a;
        double r1441390 = r1441388 * r1441389;
        double r1441391 = r1441381 * r1441390;
        double r1441392 = r1441387 + r1441391;
        double r1441393 = sqrt(r1441392);
        double r1441394 = r1441386 - r1441393;
        double r1441395 = r1441394 / r1441389;
        double r1441396 = 0.5;
        double r1441397 = r1441395 * r1441396;
        double r1441398 = r1441378 / r1441389;
        double r1441399 = r1441382 - r1441398;
        double r1441400 = r1441385 ? r1441397 : r1441399;
        double r1441401 = r1441380 ? r1441383 : r1441400;
        return r1441401;
}

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

Original33.3
Target20.4
Herbie9.7
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -5.7874989996849275e-40

    1. Initial program 53.7

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

    2. Taylor expanded around -inf 7.3

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

    3. Simplified7.3

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

    if -5.7874989996849275e-40 < b < 1.7665622931893247e+83

    1. Initial program 13.8

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

    3. Applied clear-num13.9

      \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity13.9

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

    6. Applied times-frac13.9

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

    7. Applied add-cube-cbrt13.9

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{2}{1} \cdot \frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]

    8. Applied times-frac13.9

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{2}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]

    9. Simplified13.9

      \[\leadsto \color{blue}{\frac{1}{2}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]

    10. Simplified13.8

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

    if 1.7665622931893247e+83 < b

    1. Initial program 42.5

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

    2. Taylor expanded around inf 3.9

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

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -5.7874989996849275 \cdot 10^{-40}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 1.7665622931893247 \cdot 10^{+83}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + c \cdot \left(-4 \cdot a\right)}}{a} \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (a b c)
  :name "quadm (p42, negative)"

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

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