jeff quadratic root 1

Average Error: 20.2 → 7.1

Time: 5.5s

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 < -5.7901015788997141e138

   1. Initial program 37.2

      \[\]

   2. Taylor expanded around -inf 6.6

      \[\leadsto \]

   3. Simplified 1.7

      \[\leadsto \]

   if -5.7901015788997141e138 < b < 5.974798443547602e57

   1. Initial program 9.0

      \[\]

   2. Simplified 9.1

      \[\leadsto \]

   if 5.974798443547602e57 < b

   1. Initial program 39.3

      \[\]

   2. Taylor expanded around inf 11.0

      \[\leadsto \]

   3. Simplified 6.0

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

4. Final simplification 7.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(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)))))))