Average Error: 35.0 → 7.5
Time: 27.6s
Precision: 64
Internal precision: 2944
\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
⬇
\[\begin{array}{l}
\mathbf{if}\;b \le -9.534865642779829 \cdot 10^{+39}:\\
\;\;\;\;\frac{\frac{4}{2} \cdot \frac{c}{1}}{\frac{a + a}{\frac{b}{c}} - \left(b - \left(-b\right)\right)}\\
\mathbf{if}\;b \le -3.6019808479897 \cdot 10^{-63}:\\
\;\;\;\;\frac{\frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\
\mathbf{if}\;b \le -3.3498534903732907 \cdot 10^{-77}:\\
\;\;\;\;\frac{\frac{4}{2} \cdot \frac{c}{1}}{\frac{a + a}{\frac{b}{c}} - \left(b - \left(-b\right)\right)}\\
\mathbf{if}\;b \le 2.479231526661392 \cdot 10^{+104}:\\
\;\;\;\;\left(\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\\
\mathbf{else}:\\
\;\;\;\;\frac{-b}{a}\\
\end{array}\]
Target
| Original | 35.0 |
|---|
| Comparison | 22.6 |
|---|
| Herbie | 7.5 |
|---|
\[ \begin{array}{l}
\mathbf{if}\;b \lt 0:\\
\;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\
\mathbf{else}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\
\end{array} \]
Derivation
- Split input into 5 regimes.
-
if b < -9.534865642779829e+39
Initial program 58.2
\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied flip-- 58.2
\[\leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied simplify 31.9
\[\leadsto \frac{\frac{\color{blue}{a \cdot \left(4 \cdot c\right)}}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
- Using strategy
rm
Applied div-inv 31.9
\[\leadsto \color{blue}{\frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}} \cdot \frac{1}{2 \cdot a}}\]
Applied taylor 14.7
\[\leadsto \frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} \cdot \frac{1}{2 \cdot a}\]
Taylor expanded around -inf 14.7
\[\leadsto \frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \color{blue}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}} \cdot \frac{1}{2 \cdot a}\]
Applied simplify 2.0
\[\leadsto \color{blue}{\frac{\frac{4}{2} \cdot \frac{c}{1}}{\frac{a + a}{\frac{b}{c}} - \left(b - \left(-b\right)\right)}}\]
if -9.534865642779829e+39 < b < -3.6019808479897e-63
Initial program 43.1
\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied flip-- 43.1
\[\leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied simplify 15.1
\[\leadsto \frac{\frac{\color{blue}{a \cdot \left(4 \cdot c\right)}}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
if -3.6019808479897e-63 < b < -3.3498534903732907e-77
Initial program 60.3
\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied flip-- 60.2
\[\leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
Applied simplify 49.9
\[\leadsto \frac{\frac{\color{blue}{a \cdot \left(4 \cdot c\right)}}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
- Using strategy
rm
Applied div-inv 50.0
\[\leadsto \color{blue}{\frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}} \cdot \frac{1}{2 \cdot a}}\]
Applied taylor 16.0
\[\leadsto \frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} \cdot \frac{1}{2 \cdot a}\]
Taylor expanded around -inf 16.0
\[\leadsto \frac{a \cdot \left(4 \cdot c\right)}{\left(-b\right) + \color{blue}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}} \cdot \frac{1}{2 \cdot a}\]
Applied simplify 9.9
\[\leadsto \color{blue}{\frac{\frac{4}{2} \cdot \frac{c}{1}}{\frac{a + a}{\frac{b}{c}} - \left(b - \left(-b\right)\right)}}\]
if -3.3498534903732907e-77 < b < 2.479231526661392e+104
Initial program 12.3
\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
- Using strategy
rm
Applied div-inv 12.4
\[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
if 2.479231526661392e+104 < b
Initial program 46.5
\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
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
\[\leadsto \color{blue}{\frac{-b}{a}}\]
- Recombined 5 regimes into one program.
- Removed slow pow expressions
Runtime
Please include this information when filing a bug report:
herbie shell --seed '#(1065003094 2074156664 2352254222 753858891 3745550101 3374585842)'
(FPCore (a b c)
:name "quadm (p42, negative)"
:target
(if (< b 0) (/ c (* a (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)))) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)))
(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)))
