jeff quadratic root 1

Average Error: 20.0 → 6.8

Time: 5.4s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Split input into 3 regimes

2. if b < -3.6812878763384508e143

   1. Initial program 36.0

      \[\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 36.0

      \[\leadsto \]

   4. Applied sqrt-prod 36.0

      \[\leadsto \]

   5. Simplified 36.0

      \[\leadsto \]

   6. Simplified 36.0

      \[\leadsto \]

   7. Taylor expanded around -inf 6.2

      \[\leadsto \]

   8. Simplified 1.6

      \[\leadsto \]

   if -3.6812878763384508e143 < b < 9.6623670239352678e49

   1. Initial program 8.7

      \[\]

   2. Simplified 8.8

      \[\leadsto \]

   if 9.6623670239352678e49 < b

   1. Initial program 38.2

      \[\]

   2. Taylor expanded around inf 10.4

      \[\leadsto \]

   3. Simplified 5.7

      \[\leadsto \]
   4. Using strategy rm

   5. Applied add-cbrt-cube 5.7

      \[\leadsto \]

   6. Simplified 5.7

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 6.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (a b c)
  :name "jeff quadratic root 1"
  :precision binary64
  (if (>= b 0.0) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)) (/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))