Error

Target

Derivation

1. Split input into 4 regimes

2. if b < -1.4471521473484649e+72

   1. Initial program 37.8

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

   2. Taylor expanded around -inf 4.2

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

   3. Applied simplify4.2

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

   if -1.4471521473484649e+72 < b < 7.555616443406063e-282

   1. Initial program 9.5

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

   3. Applied div-inv9.7

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

   if 7.555616443406063e-282 < b < 1.1498155483847317e+81

   1. Initial program 31.3

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

   3. Applied flip-+31.4

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

   4. Applied simplify15.0

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

   6. Applied *-un-lft-identity15.0

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

   7. Applied times-frac15.0

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

   8. Applied times-frac15.0

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

   9. Applied simplify15.0

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

   10. Applied simplify7.7

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

   if 1.1498155483847317e+81 < b

   1. Initial program 57.3

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

   2. Taylor expanded around inf 13.9

      \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]

   3. Applied simplify3.0

      \[\leadsto \color{blue}{\frac{c}{b} \cdot \frac{-2}{2}}\]
3. Recombined 4 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed '#(1063027428 1192549564 1443466578 604016274 3637110559 1698629644)' 
(FPCore (a b c)
  :name "The quadratic formula (r1)"

  :herbie-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)))