Average Error: 33.9 → 5.9
Time: 1.1m
Precision: 64
Internal precision: 3200
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
⬇
\[\begin{array}{l}
\mathbf{if}\;b \le -5.224339320607286 \cdot 10^{+142}:\\
\;\;\;\;\frac{-b}{a}\\
\mathbf{if}\;b \le -2.21585542402177 \cdot 10^{-292}:\\
\;\;\;\;\frac{b + \left(-\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}\right)}{-2 \cdot a}\\
\mathbf{if}\;b \le 1.1333439556022532 \cdot 10^{+108}:\\
\;\;\;\;\frac{1}{\frac{2}{c \cdot 4} \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}\right)}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{b} \cdot \frac{-2}{2}\\
\end{array}\]
Target
| Original | 33.9 |
|---|
| Comparison | 21.3 |
|---|
| Herbie | 5.9 |
|---|
\[ \begin{array}{l}
\mathbf{if}\;b \lt 0:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\
\end{array} \]
Derivation
- Split input into 4 regimes.
-
if b < -5.224339320607286e+142
Initial program 57.8
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Applied taylor 0
\[\leadsto -1 \cdot \frac{b}{a}\]
Taylor expanded around -inf 0
\[\leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
Applied simplify 0
\[\leadsto \color{blue}{\frac{-b}{a}}\]
if -5.224339320607286e+142 < b < -2.21585542402177e-292
Initial program 8.6
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied frac-2neg 8.6
\[\leadsto \color{blue}{\frac{-\left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}{-2 \cdot a}}\]
Applied simplify 8.7
\[\leadsto \frac{\color{blue}{b + \left(-\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}\right)}}{-2 \cdot a}\]
if -2.21585542402177e-292 < b < 1.1333439556022532e+108
Initial program 31.4
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied flip-+ 31.5
\[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied simplify 15.8
\[\leadsto \frac{\frac{\color{blue}{\left(c \cdot a\right) \cdot 4}}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
- Using strategy
rm
Applied clear-num 16.0
\[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\frac{\left(c \cdot a\right) \cdot 4}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}}\]
Applied simplify 9.5
\[\leadsto \frac{1}{\color{blue}{\frac{2}{c \cdot 4} \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}\right)}}\]
if 1.1333439556022532e+108 < b
Initial program 59.8
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Applied taylor 14.7
\[\leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
Taylor expanded around inf 14.7
\[\leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
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 '#(1068028399 4028058041 2917032441 2563479541 765645300 1132738916)'
(FPCore (a b c)
:name "quadp (p42, positive)"
: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)))
