Quadratic roots, narrow range

Average Error: 28.6 → 16.2

Time: 6.0s

Precision: binary64

\[\]

Math

\[\]

↓

\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Split input into 2 regimes

2. if b < 1265.74682565733906

   1. Initial program 17.3

      \[\]

   2. Simplified 17.3

      \[\leadsto \]
   3. Using strategy rm

   4. Applied flip-- 17.4

      \[\leadsto \]

   5. Simplified 16.4

      \[\leadsto \]

   6. Simplified 16.4

      \[\leadsto \]

   if 1265.74682565733906 < b

   1. Initial program 36.6

      \[\]

   2. Simplified 36.6

      \[\leadsto \]

   3. Taylor expanded around inf 16.1

      \[\leadsto \]

   4. Simplified 16.1

      \[\leadsto \]
   5. Using strategy rm

   6. Applied clear-num 16.1

      \[\leadsto \]

   7. Simplified 16.1

      \[\leadsto \]
3. Recombined 2 regimes into one program.

4. Final simplification 16.2

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b c)
  :name "Quadratic roots, narrow range"
  :precision binary64
  :pre (and (< 1.0536712127723509e-08 a 94906265.62425156) (< 1.0536712127723509e-08 b 94906265.62425156) (< 1.0536712127723509e-08 c 94906265.62425156))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))