Error

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Target

Derivation

1. Split input into 4 regimes

2. if b < -1.7715196556134555e+46

   1. Initial program 56.2

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

   2. Taylor expanded around -inf 56.2

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

   3. Taylor expanded around -inf 4.3

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

   4. Simplified4.3

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

   if -1.7715196556134555e+46 < b < -1.1090157738250754e-76

   1. Initial program 42.2

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

   2. Taylor expanded around -inf 42.2

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

   4. Applied flip--42.3

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

   5. Applied associate-/l/45.0

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

   6. Simplified18.1

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

   if -1.1090157738250754e-76 < b < 5.973421650485517e+105

   1. Initial program 13.0

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

   2. Taylor expanded around -inf 13.0

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

   if 5.973421650485517e+105 < b

   1. Initial program 46.5

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

   2. Taylor expanded around inf 3.8

      \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
3. Recombined 4 regimes into one program.

4. Final simplification9.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.7715196556134555 \cdot 10^{+46}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le -1.1090157738250754 \cdot 10^{-76}:\\ \;\;\;\;\frac{\left(a \cdot c\right) \cdot 4}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{{b}^{2} - \left(a \cdot c\right) \cdot 4}\right)}\\ \mathbf{elif}\;b \le 5.973421650485517 \cdot 10^{+105}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{{b}^{2} - \left(a \cdot c\right) \cdot 4}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 
(FPCore (a b c)
  :name "The quadratic formula (r2)"

  :herbie-target
  (if (< b 0) (/ c (* a (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))) (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))

  (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))

Details

Time bar (total: 24.4s)Debug log