Average Error: 34.5 → 6.9
Time: 23.9s
Precision: 64
Internal precision: 2944
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
⬇
\[\begin{array}{l}
\mathbf{if}\;b \le -1.6429991956785702 \cdot 10^{+85}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\
\mathbf{if}\;b \le 1.964481890400044 \cdot 10^{-184}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\
\mathbf{if}\;b \le 2.4861451900721143 \cdot 10^{+28}:\\
\;\;\;\;\frac{a}{2} \cdot \frac{\frac{4 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{b} \cdot \frac{-2}{2}\\
\end{array}\]
Target
| Original | 34.5 |
|---|
| Comparison | 21.9 |
|---|
| Herbie | 6.9 |
|---|
\[ \begin{array}{l}
\mathbf{if}\;b \lt 0:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\
\end{array} \]
Derivation
- Split input into 4 regimes.
-
if b < -1.6429991956785702e+85
Initial program 42.7
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Applied taylor 11.7
\[\leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
Taylor expanded around -inf 11.7
\[\leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
Applied simplify 0.0
\[\leadsto \color{blue}{\frac{\frac{c}{b}}{1} - \frac{b}{a}}\]
Applied simplify 0.0
\[\leadsto \color{blue}{\frac{c}{b}} - \frac{b}{a}\]
if -1.6429991956785702e+85 < b < 1.964481890400044e-184
Initial program 10.6
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
if 1.964481890400044e-184 < b < 2.4861451900721143e+28
Initial program 32.3
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied flip-+ 32.4
\[\leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied simplify 16.5
\[\leadsto \frac{\frac{\color{blue}{a \cdot \left(4 \cdot c\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
- Using strategy
rm
Applied *-un-lft-identity 16.5
\[\leadsto \frac{\frac{a \cdot \left(4 \cdot c\right)}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}}{2 \cdot a}\]
Applied times-frac 12.6
\[\leadsto \frac{\color{blue}{\frac{a}{1} \cdot \frac{4 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied times-frac 20.3
\[\leadsto \color{blue}{\frac{\frac{a}{1}}{2} \cdot \frac{\frac{4 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}}\]
Applied simplify 20.3
\[\leadsto \color{blue}{\frac{a}{2}} \cdot \frac{\frac{4 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}\]
if 2.4861451900721143e+28 < b
Initial program 57.8
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Applied taylor 15.1
\[\leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
Taylor expanded around inf 15.1
\[\leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
Applied simplify 0
\[\leadsto \color{blue}{\frac{c}{b} \cdot \frac{-2}{2}}\]
- Recombined 4 regimes into one program.
- Removed slow pow expressions
Runtime
Please include this information when filing a bug report:
herbie shell --seed '#(1064651971 495577305 2200811460 13024471 864198081 231948279)'
(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)))
