Error

Target

Derivation

1. Split input into 4 regimes.

2. if b < -4.319226994044875e+67

   1. Initial program 43.2

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

   2. Applied taylor 0

      \[\leadsto -1 \cdot \frac{b}{a}\]

   3. Taylor expanded around -inf 0

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

   4. Applied simplify 0

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

   if -4.319226994044875e+67 < b < 1.3254506382963175e-308

   1. Initial program 9.8

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

   3. Applied clear-num 9.9

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

   if 1.3254506382963175e-308 < b < 1.0905893076356243e+100

   1. Initial program 31.4

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

   3. Applied flip-+ 31.5

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

   4. Applied simplify 16.5

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

   6. Applied *-un-lft-identity 16.5

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

   7. Applied times-frac 16.5

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

   8. Applied times-frac 16.5

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

   9. Applied simplify 16.5

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

   10. Applied simplify 9.2

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

   if 1.0905893076356243e+100 < b

   1. Initial program 58.9

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

   2. Applied taylor 40.7

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

   3. Taylor expanded around inf 40.7

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

   4. Applied simplify 0

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

   5. Applied simplify 0

      \[\leadsto \frac{b + \left(-b\right)}{a + a} - \color{blue}{\frac{c}{b}}\]
3. Recombined 4 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 1.3m) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2170345737 194459988 47475974 1804353289 669403722 2564614823)'
(FPCore (a b c)
  :name "The quadratic formula (r1)"

  :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)))