Average Error: 33.7 → 8.3
Time: 24.5s
Precision: 64
Internal precision: 2688
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
⬇
\[\begin{array}{l} \mathbf{if}\;b \le -1.2104515124530692 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{if}\;b \le 5.753459880179216 \cdot 10^{-171}:\\ \;\;\;\;\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\\ \mathbf{if}\;b \le 2.3106113327966147 \cdot 10^{+121}:\\ \;\;\;\;\frac{\frac{\left(c \cdot a\right) \cdot 4}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot \frac{-2}{2}\\ \end{array}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Target

Original33.7
Comparison21.2
Herbie8.3
\[ \begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array} \]

Derivation

  1. Split input into 4 regimes.

  2. if b < -1.2104515124530692e+151

    1. Initial program 59.2

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

    2. Applied taylor 13.0

      \[\leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]

    3. Taylor expanded around -inf 13.0

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

    4. Applied simplify 0.0

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

    5. Applied simplify 0.0

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

    if -1.2104515124530692e+151 < b < 5.753459880179216e-171

    1. Initial program 10.3

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

    3. Applied div-inv 10.5

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

    if 5.753459880179216e-171 < b < 2.3106113327966147e+121

    1. Initial program 37.7

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

    3. Applied flip-+ 37.8

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

    4. Applied simplify 15.5

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

    if 2.3106113327966147e+121 < b

    1. Initial program 60.2

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

    2. Applied taylor 15.8

      \[\leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]

    3. Taylor expanded around inf 15.8

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

    4. Applied simplify 0

      \[\leadsto \color{blue}{\frac{c}{b} \cdot \frac{-2}{2}}\]
  3. Recombined 4 regimes into one program.
  4. Removed slow pow expressions

Runtime

Time bar (total: 24.5s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067901057 3396600083 3715501224 3126139233 3908045574 1593683916)'
(FPCore (a b c)
  :name "quadp (p42, positive)"

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

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