Average Error: 35.1 → 5.6
Time: 19.4s
Precision: 64
Internal precision: 2688
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
⬇
\[\begin{array}{l}
\mathbf{if}\;b \le -3.7179117657221714 \cdot 10^{+53}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\
\mathbf{if}\;b \le -8.130671812374203 \cdot 10^{-266}:\\
\;\;\;\;\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\\
\mathbf{if}\;b \le 3.5012060427894713 \cdot 10^{+160}:\\
\;\;\;\;\frac{1}{2} \cdot \frac{c \cdot 4}{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{b} \cdot \frac{-2}{2}\\
\end{array}\]
Target
| Original | 35.1 |
|---|
| Comparison | 22.4 |
|---|
| Herbie | 5.6 |
|---|
\[ \begin{array}{l}
\mathbf{if}\;b \lt 0:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\
\end{array} \]
Derivation
- Split input into 4 regimes.
-
if b < -3.7179117657221714e+53
Initial program 41.1
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Applied taylor 10.7
\[\leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
Taylor expanded around -inf 10.7
\[\leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
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 -3.7179117657221714e+53 < b < -8.130671812374203e-266
Initial program 9.7
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied div-inv 9.9
\[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
if -8.130671812374203e-266 < b < 3.5012060427894713e+160
Initial program 34.1
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied flip-+ 34.2
\[\leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied simplify 16.6
\[\leadsto \frac{\frac{\color{blue}{a \cdot \left(4 \cdot c\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
- Using strategy
rm
Applied *-un-lft-identity 16.6
\[\leadsto \frac{\color{blue}{1 \cdot \frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied times-frac 16.6
\[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{\frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}}\]
Applied simplify 8.7
\[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{c \cdot 4}{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}}}\]
if 3.5012060427894713e+160 < b
Initial program 62.9
\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Applied taylor 16.1
\[\leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
Taylor expanded around inf 16.1
\[\leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
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 '#(1067488128 1186562765 67428877 2948030040 4169093828 3206893112)'
(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)))
